5 · P(7, 4) · C(10, 3) The Department of Foreign Languages of a liberal arts college conducted a survey of its recent graduates to determine the foreign language courses they had taken while undergraduates at the college. Of the 550 graduates 206 had at least one year of Spanish. 178 had at least one year of French. 141 had at least one year of German. 44 had at least one year of Spanish and French. 32 had at least one year of Spanish and German. 25 had at least one year of French and German. 9 had at least one year of all three languages. (a) How many of the graduates had at least 1 yr of at least one of the three languages? graduates (b) How many of the graduates had at least 1 yr of exactly one of the three languages? graduates (c) How many of the graduates had less than 1 yr of any of the three languages? graduates In how many ways can 7 different compact discs be arranged on a shelf? ways In how many ways can 3 pictures be selected from a group of nine different pictures? ways How many three-digit numbers can be formed from the numerals in the set {1, 2, 3, 4, 5, 6, 7} if the following is true? (a) Repetition of digits is not allowed numbers (b) Repetition of digits is allowed numbers 4 soups, 32 entrées, and 2 desserts are listed on the "Special" menu at the Neptune Restaurant. How many different selections consisting of one soup, one entrée, and one dessert can a customer choose from this menu? different selections In a survey conducted by Helena, a financial consultant, it was revealed of her 412 clients 281 own stocks. 190 own bonds. 181 own mutual funds. 117 own both stocks and bonds. 106 own both stocks and mutual funds. 103 own both bonds and mutual funds. How many of Helena's clients own stocks, bonds, and mutual funds? (Assume each client invested in at least one of the three types of funds.) clients In an election being held by the Associated Students Organization, there are seven candidates for president, five for vice-president, four for secretary, and six for treasurer. How many different possible outcomes are there for this election? outcomes There are 10 seniors and 6 juniors in the Math Club at Jefferson High School. In how many ways can a math team consisting of four seniors and three juniors be selected from members of the Math Club? ways From a shipment of 75 transistors, 6 of which are defective, a sample of 4 transistors is selected at random. (a) In how many different ways can the sample be selected? ways (b) How many samples contain exactly 3 defective transistors? samples (c) How many samples do not contain any defective transistors? samples A sample of 3 balls is to be selected at random from an urn containing 20 balls numbered 1 to 20. Five balls are green, 6 balls are white, and 9 balls are black. (a) How many different samples can be selected? samples (b) How many samples can be selected that contain at least 1 white ball? samples Let S be any sample space, and let E and F be any two events associated with the experiment. Describe the events using the symbols ∪, ∩, and c. The event that E but not F occurs An experiment consists of spinning the hand of the numbered disc shown in the following figure and then observing the region in which the pointer stops. (If the needle stops on a line, the result is discounted and the needle is spun again. Enter ∅ for the empty set.) (a) What is the appropriate sample space S for this experiment? S = (b) Describe the event E "the spinner points to the number 3." E = (c) Describe the event F "the spinner points to an odd number Let S = {3, 8, 13, 18, 23, 28}, E = {8, 18, 28}, F = {3, 13, 23},and G = {23, 28}. (Enter ∅ for the empty set.) Find the event E ∩ F ∩ G. Let S = {d, g, l, r, s, x} be a sample space of an experiment and let E = {d, g}, F = {d, r, x}, and G = {g, l, s} be events of this experiment. (Enter ∅ for the empty set.) Find the events Ec and Fc ∩ G. Ec = Fc ∩ G = Let S = {4, 9, 14, 19, 24, 29}, E = {9, 19, 29}, F = {4, 14, 24}, and G = {24, 29}. (Enter ∅ for the empty set.) Find the event (E ∩ F ∩ G)c. Let S = {a, h, k, r, u, y} be a sample space of an experiment and let E = {a, h} and F = {a, r, y} be events of this experiment. (Enter ∅ for the empty set.) Find the events E ∪ F and E ∩ F. Let S = {c, h, j, p, v, y} be a sample space of an experiment and let F = {c, p, y} and G = {h, j, v} be events of this experiment. (Enter ∅ for the empty set.) Find the events F ∪ G and F ∩ G.

5 · P(7, 4) · C(10, 3) The Department of Foreign Languages of a liberal arts college conducted a survey of its recent graduates to determine the foreign language courses they had taken while undergraduates at the college. Of the 550 graduates 206 had at least one year of Spanish. 178 had at least one year of French. 141 had at least one year of German. 44 had at least one year of Spanish and French. 32 had at least one year of Spanish and German. 25 had at least one year of French and German. 9 had at least one year of all three languages. (a) How many of the graduates had at least 1 yr of at least one of the three languages? graduates (b) How many of the graduates had at least 1 yr of exactly one of the three languages? graduates (c) How many of the graduates had less than 1 yr of any of the three languages? graduates In how many ways can 7 different compact discs be arranged on a shelf? ways In how many ways can 3 pictures be selected from a group of nine different pictures? ways How many three-digit numbers can be formed from the numerals in the set {1, 2, 3, 4, 5, 6, 7} if the following is true? (a) Repetition of digits is not allowed numbers (b) Repetition of digits is allowed numbers 4 soups, 32 entrées, and 2 desserts are listed on the "Special" menu at the Neptune Restaurant. How many different selections consisting of one soup, one entrée, and one dessert can a customer choose from this menu? different selections In a survey conducted by Helena, a financial consultant, it was revealed of her 412 clients 281 own stocks. 190 own bonds. 181 own mutual funds. 117 own both stocks and bonds. 106 own both stocks and mutual funds. 103 own both bonds and mutual funds. How many of Helena's clients own stocks, bonds, and mutual funds? (Assume each client invested in at least one of the three types of funds.) clients In an election being held by the Associated Students Organization, there are seven candidates for president, five for vice-president, four for secretary, and six for treasurer. How many different possible outcomes are there for this election? outcomes There are 10 seniors and 6 juniors in the Math Club at Jefferson High School. In how many ways can a math team consisting of four seniors and three juniors be selected from members of the Math Club? ways From a shipment of 75 transistors, 6 of which are defective, a sample of 4 transistors is selected at random. (a) In how many different ways can the sample be selected? ways (b) How many samples contain exactly 3 defective transistors? samples (c) How many samples do not contain any defective transistors? samples A sample of 3 balls is to be selected at random from an urn containing 20 balls numbered 1 to 20. Five balls are green, 6 balls are white, and 9 balls are black. (a) How many different samples can be selected? samples (b) How many samples can be selected that contain at least 1 white ball? samples Let S be any sample space, and let E and F be any two events associated with the experiment. Describe the events using the symbols ∪, ∩, and c. The event that E but not F occurs An experiment consists of spinning the hand of the numbered disc shown in the following figure and then observing the region in which the pointer stops. (If the needle stops on a line, the result is discounted and the needle is spun again. Enter ∅ for the empty set.) (a) What is the appropriate sample space S for this experiment? S = (b) Describe the event E "the spinner points to the number 3." E = (c) Describe the event F "the spinner points to an odd number Let S = {3, 8, 13, 18, 23, 28}, E = {8, 18, 28}, F = {3, 13, 23},and G = {23, 28}. (Enter ∅ for the empty set.) Find the event E ∩ F ∩ G. Let S = {d, g, l, r, s, x} be a sample space of an experiment and let E = {d, g}, F = {d, r, x}, and G = {g, l, s} be events of this experiment. (Enter ∅ for the empty set.) Find the events Ec and Fc ∩ G. Ec = Fc ∩ G = Let S = {4, 9, 14, 19, 24, 29}, E = {9, 19, 29}, F = {4, 14, 24}, and G = {24, 29}. (Enter ∅ for the empty set.) Find the event (E ∩ F ∩ G)c. Let S = {a, h, k, r, u, y} be a sample space of an experiment and let E = {a, h} and F = {a, r, y} be events of this experiment. (Enter ∅ for the empty set.) Find the events E ∪ F and E ∩ F. Let S = {c, h, j, p, v, y} be a sample space of an experiment and let F = {c, p, y} and G = {h, j, v} be events of this experiment. (Enter ∅ for the empty set.) Find the events F ∪ G and F ∩ G.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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5 · P(7, 4) · C(10, 3)

The Department of Foreign Languages of a liberal arts college conducted a survey of its recent graduates to determine the foreign language courses they had taken while undergraduates at the college. Of the 550 graduates

206	had at least one year of Spanish.
178	had at least one year of French.
141	had at least one year of German.
44	had at least one year of Spanish and French.
32	had at least one year of Spanish and German.
25	had at least one year of French and German.
9	had at least one year of all three languages.

(a) How many of the graduates had at least 1 yr of at least one of the three languages?
graduates
(b) How many of the graduates had at least 1 yr of exactly one of the three languages?
graduates
(c) How many of the graduates had less than 1 yr of any of the three languages?
graduates

In how many ways can 7 different compact discs be arranged on a shelf?
ways
In how many ways can 3 pictures be selected from a group of nine different pictures?
ways
How many three-digit numbers can be formed from the numerals in the set {1, 2, 3, 4, 5, 6, 7} if the following is true?
(a) Repetition of digits is not allowed
numbers
(b) Repetition of digits is allowed
numbers
4 soups, 32 entrées, and 2 desserts are listed on the "Special" menu at the Neptune Restaurant. How many different selections consisting of one soup, one entrée, and one dessert can a customer choose from this menu?
different selections
In a survey conducted by Helena, a financial consultant, it was revealed of her 412 clients
281 own stocks.
190 own bonds.
181 own mutual funds.
117 own both stocks and bonds.
106 own both stocks and mutual funds.
103 own both bonds and mutual funds.
How many of Helena's clients own stocks, bonds, and mutual funds? (Assume each client invested in at least one of the three types of funds.)
clients
In an election being held by the Associated Students Organization, there are seven candidates for president, five for vice-president, four for secretary, and six for treasurer. How many different possible outcomes are there for this election?
outcomes
There are 10 seniors and 6 juniors in the Math Club at Jefferson High School. In how many ways can a math team consisting of four seniors and three juniors be selected from members of the Math Club?
ways
From a shipment of 75 transistors, 6 of which are defective, a sample of 4 transistors is selected at random.
(a) In how many different ways can the sample be selected?
ways
(b) How many samples contain exactly 3 defective transistors?
samples
(c) How many samples do not contain any defective transistors?
samples
A sample of 3 balls is to be selected at random from an urn containing 20 balls numbered 1 to 20. Five balls are green, 6 balls are white, and 9 balls are black.
(a) How many different samples can be selected?
samples
(b) How many samples can be selected that contain at least 1 white ball?
samples
Let S be any sample space, and let E and F be any two events associated with the experiment. Describe the events using the symbols ∪, ∩, and ^c.
The event that E but not F occurs
An experiment consists of spinning the hand of the numbered disc shown in the following figure and then observing the region in which the pointer stops. (If the needle stops on a line, the result is discounted and the needle is spun again. Enter ∅ for the empty set.)
(a) What is the appropriate sample space S for this experiment?

S =

(b) Describe the event E "the spinner points to the number 3."

E =
(c) Describe the event F "the spinner points to an odd number
Let S = {3, 8, 13, 18, 23, 28}, E = {8, 18, 28}, F = {3, 13, 23},and G = {23, 28}. (Enter ∅ for the empty set.)
Find the event E ∩ F ∩ G.
Let S = {d, g, l, r, s, x} be a sample space of an experiment and let E = {d, g}, F = {d, r, x}, and G = {g, l, s} be events of this experiment. (Enter ∅ for the empty set.)
Find the events E^c and F^c ∩ G.

E^c
=

F^c ∩ G
=
Let S = {4, 9, 14, 19, 24, 29}, E = {9, 19, 29}, F = {4, 14, 24}, and G = {24, 29}. (Enter ∅ for the empty set.)
Find the event (E ∩ F ∩ G)^c.
Let S = {a, h, k, r, u, y} be a sample space of an experiment and let E = {a, h} and F = {a, r, y} be events of this experiment. (Enter ∅ for the empty set.)
Find the events E ∪ F and E ∩ F.
Let S = {c, h, j, p, v, y} be a sample space of an experiment and let F = {c, p, y} and G = {h, j, v} be events of this experiment. (Enter ∅ for the empty set.)
Find the events F ∪ G and F ∩ G.

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