30 ||| V Permutations and combinations: Problem type 2 Answer the questions below. (a) There are 15 European cities that Melissa would eventually like to visit. On her next vacation, though, she only has time to visit 3 of the cities: one on Monday, one on Tuesday, and one on Wednesday. She is now trying to make a schedule of which city she'll visit on which day. How many different schedules are possible? (Assume that she will not visit a city more than once.) 0 (b) A certain committee consists of 17 people. From the committee, a president, a vice-president, a secretary, and a treasurer are to be chosen. In how many ways can these 4 offices be filled? Assume that a committee member can hold at most one of these offices. 0 Explanation A B Q BEL 12 ko W S Check 0 59. F2 # 3 LU E 20 F3 $ 4 NOV 26 F4 R F DO LO 5 S T G F6 tv N & 7 H F7 2023 McGraw Hill LLC. All Rights Reserved. U X 3 all A A R

30 ||| V Permutations and combinations: Problem type 2 Answer the questions below. (a) There are 15 European cities that Melissa would eventually like to visit. On her next vacation, though, she only has time to visit 3 of the cities: one on Monday, one on Tuesday, and one on Wednesday. She is now trying to make a schedule of which city she'll visit on which day. How many different schedules are possible? (Assume that she will not visit a city more than once.) 0 (b) A certain committee consists of 17 people. From the committee, a president, a vice-president, a secretary, and a treasurer are to be chosen. In how many ways can these 4 offices be filled? Assume that a committee member can hold at most one of these offices. 0 Explanation A B Q BEL 12 ko W S Check 0 59. F2 # 3 LU E 20 F3 $ 4 NOV 26 F4 R F DO LO 5 S T G F6 tv N & 7 H F7 2023 McGraw Hill LLC. All Rights Reserved. U X 3 all A A R

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Note: In this problem set, the notation C(n, k) is used for the combination "n choose k." Alternate notation: ( ) 16.) A group of 2 professors and 5 students (3 grad students and 2 undergrads) go to a movie together. The professors want to sit together, and the grad students want to sit together. How many ways are there to seat this group in a row of 7 seats?
Question 3 An ice-cream shop offers a selection of 6 different cones, 8 different flavors, and 7 different toppings. How many different combinations of ice-creams consisting of one cone, one flavor, and one topping are possible to create given the assortment?
Consider a 6 vs 6 youth soccer team (i.e., teams field 6 players at once) with 9 players. (a) How many different combinations of players can the team field? (b) If the team has exactly one goalie (who has to play), how many different combinations of players can the team field? (c) If the team has exactly two goalie (exactly one of which has to play and the other cannot), how many different combinations of players can the team field?
A survey of 145 college students was done to find out what elective courses they were taking. Let A=the set of those taking art, B= the set of those taking basketweaving, and C= the set of those taking canoeing. The study revealed the following information.n(A)= 45n(B)= 55n(C)=40n(AnB)= 12n(AnC)= 15n(BnC)= 23n(AnBnC)= 2 How many students were not taking any of these electives?
A horticulturist crosses two plants of the same species-one has a red flower and the other has a white flower. He knows from genetics that of the resulting seeds will produce plants with white flowers and will produce plants with red flowers. He harvests seeds and grows out 700 plants. How many of those would he expect to produce white flowers? (Simplify your answer completely.) plants How many of those would he expect to produce red flowers? (Simplify your answer completely.) plants
Problem:Fifteen books are to be placed in a shelf. The fifteen books are composed of the following: six structural engineering books, five geotechnical engineering books, and four water-resource engineering books. 1. In how many ways can you arrange the books if they must be grouped together? 2. In how many ways can you arrange the books if the geotechnical engineering books are grouped together?
A company is organizing a team-building event with various activities. There are 12 employees attending the event, and they need to be split into three teams: Team A, Team B, and Team C. Each team should have at least 2 members but no more than 6 members. In how many different ways can the teams be formed? (Note: The order of the teams doesn't matter; i.e., Team A, Team B, and Team C is the same as Team C, Team A, and Team B.)
a. A teacher creating a quiz has to decide how to order the problems—if there are tenproblems, how many different ways can they be ordered?b. How many ways can the problems be ordered if the teacher decides to put the one essay question either first or last?c. If it's decided the test is too long, how many ways could the teacher choose 8 of the problems to create a shorter quiz?
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6. A lead role and a supporting role are to be chosen from a drama club consisting of 40 talents. How many various choices of actors are possible if: there are no restrictions? ( (1) (ii) actor Kristoff will participate only if he is the lead role? ( (ii) actors Jess and Jet will act together or not at all? (iv) actors Keanne and Gian will not act together?