Concept explainers
Counting Methods. Answer the following questions us-
ing the appropriate counting technique. which may be either
arrangements with repetition. permutations. Or combinations.
Be sure to explain why this counting technique applies to the
problem.
23. HOW many different nine-digit ZIP codes can be formed?
24. How many different six-character can formed
from the lowercase letters of the ?
25. HOW many different six-character passwords can formed
from the lowercase letters of the alphabet if repetition is not
allowed?
26. A city council with eight members must elect a
executive committee consisting of a mayor, secretary, and
treasurer. How many executive committees are possible?
27. How many ways can the eight performances at a piano recital
be ordered?
28. A city council with ten members must appoint a four-person
subcommittee. How many subcommittees are possible?
29. Suppose you have 15 CDs from which you 6 CDs to
put in the CD player in your car. If you are not particular
about the order, how many O-CD sets are possible?
30.HOW many 6-person can be formed from a & player
volleyball assuming every player can be assign to
any position?
31. How many different birth orders with respect to gender
possible in a family with five children? (For example.
and BGBGG are different orders.)
32. HOW many different 5-cards can be dealt from a 52-card
deck?
33. How many license plates can be made of the form XX—YYYY,
where X is a letter Of the and Y is a numeral 0—9?
34. How many different groups of balls can drawn from
a barrel containing balls numbered 1—36?
35. How many different telephone numbers of the form aaa-bbb-
cccc formed if the area code cannot contain 0 and
the prefix bbb cannot contain 9?
36. HOW many anagrams (rearrangements) Of the letters
ILOVEMATH can nuke?
37. How many different three-letter “words”- can formed from
the ACGT?
38. The debate club has 18 members, but only 4 can compete
at the next meet. How many 4-Frson teams are possible?
39. A recording engineer wants to make a CD With 12 songs. In
how many different ways can the CD nude?
40. A shelter is giving away 15 but you have
room for only 4 of them. How many different families
could you have?
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Check out a sample textbook solutionChapter 7 Solutions
EBK USING AND UNDERSTANDING MATHEMATICS
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- The only problems I need help with ae the last 8 ones, Thanksarrow_forwardPrice (S) The graph below depicts a firm with market power. In the graph, MC represents the firm's marginal costs, ATC represents the average total costs, D represents demand, and MR represents marginal revenue. 110 70 60 50 40 30 20 MC ATC D 0 40 50 70 80 95 Quantity/Units MR a. At 60 units of output, how much would this profit-maximizing monopolist charge? b. How many units would it produce to maximize total revenue rather than total profit? c. What is the maximum quantity this firm can produce without incurring economic losses? d. Calculate the firm's profit at the profit-maximizing output and price. e. Why is this firm's marginal revenue curve below its demand curve? Explain.arrow_forwardA well-known company predominantly makes flat pack furniture for students. Variability with the automated machinery means the wood components are cut with a standard deviation in length of 0.45 mm. After they are cut the components are measured. If their length is more than 1.2 mm from the required length, the components are rejected. a) Calculate the percentage of components that get rejected. b) In a manufacturing run of 1000 units, how many are expected to be rejected? c) The company wishes to install more accurate equipment in order to reduce the rejection rate by one-half, using the same ±1.2mm rejection criterion. Calculate the maximum acceptable standard deviation of the new process.arrow_forward
- Let a = (-1, -2, -3) and 6 = (-4, 0, 1). Find the component of b onto a.arrow_forwardForces of 9 pounds and 15 pounds act on each other with an angle of 72°. The magnitude of the resultant force The resultant force has an angle of pounds. * with the 9 pound force. The resultant force has an angle of with the 15 pound force. It is best to calculate each angle separately and check by seeing if they add to 72°.arrow_forward1. Sketch the following sets and determine which are domains: (a) |z−2+i| ≤ 1; - (c) Imz> 1; (e) 0≤ arg z≤ л/4 (z ± 0); Ans. (b), (c) are domains. (b) |2z+3| > 4; (d) Im z = 1; - (f) | z − 4| ≥ |z.arrow_forward
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