Note: In this problem set, the notation C(n, k) is used for the combination "n choose k." Alternate notation: ( ) For Questions 12: A panel of 4 Democratic candidates, 4 Republican candidates, and 2 Independent candidates will participate in a political forum. 12.) How many working groups of 5 candidates can be formed if: (a) there must be 2 Democr

Note: In this problem set, the notation C(n, k) is used for the combination "n choose k." Alternate notation: ( ) For Questions 12: A panel of 4 Democratic candidates, 4 Republican candidates, and 2 Independent candidates will participate in a political forum. 12.) How many working groups of 5 candidates can be formed if: (a) there must be 2 Democr

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...

See similar textbooks

Similar questions

Suppose that Jeremy is a highschool science teacher and that he is dividing 16 students in his advanced chemistry class into four groups of four for a lab activity. Each of the four lab groups has been assigned its own task to complete for the activity, but the students are not assigned specific roles within the group. How many different ways can Jeremy assign his students to the four lab groups?
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?
Note: In this problem set, the notation C(n, k) is used for the combination "n choose k." Alternate notation: ( ) For the rest of the problems in this section, decide whether to use permutations or combinations. 6.) From a group of 12 newly hired office workers, 4 assistants are selected. Each of 4 different managers will be assigned one of these assistants. In how many ways can the assistants be selected and assigned?
You have one pile of 11 building blocks, each one a different color, and you also have another pile of 7 blocks, again each one a different color. How many ways are there to build a tower 4 blocks high from the first pile and another tower 3 blocks high from the second pile? Assume that the colors at each level of a tower matter. (A) 318 (B) C(11,4) C(7, 3) (C) P(11,4) P(7,3) (D) P(18,7) (E) 311 (F) C(18,7) (G) P(11,4)+ P(7,3) (H) C(11,4)+ C(7,3) O A OB OC O E O F OG H.
Suppose there are 5 men and 8 women qualified to be members of a new committee of 6 people, includinga president, a vice-president, and a secretary.(a) How many different ways do you have to pick a president, vice-president and secretary if you need atleast 1 men and 1 women? Does the order matter? Why?(b) How many different committees can you form with at least 3 women? Does the order matter? Why?
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?
An instructor gives an exam with twenty questions. Students are allowed to choose any fifteen questions to answer. (a) How many different choices of fifteen questions are there? (b) Suppose nine questions require coding and eleven do not. (i) How many groups of fifteen questions contain seven that require coding and eight that do not? (ii) How many groups of fifteen questions contain at most eight that require coding? (c) Suppose the exam instruction specifies that at most one of questions 1 and 2 MAY BE included among the fifteen. How many different choices of fifteen questions are there? (d) Suppose the exam instruction specifies that either both questions 1 and 2 are to be included among the ten or neither is to be included. How many different choices of ten questions are there?
Note: In this problem set, the notation C(n, k) is used for the combination "n choose k." Alternate notation: ( ) 2.) (a) In how many ways can a hand of 6 hearts be chosen from an ordinary deck? (b) In how many ways can a hand of 6 black cards be chosen from an ordinary deck?
Say the football team F, the basketball team B, and the track team T, decide to form a varsity club V. How many members will V have if n(F)=25, n(B)=12, n(T)=30, and no person belongs to at least two teams?
During a special promotion, a customer purchasing a computer and a printer is given a choice of 3 free software packages. There are 10 different software packages from which to select. How many different groups of software packages can be selected? Hint: This is a Combination problem! 120 604,800 360 720
A computer programming team has 15 members consisting of eight robots and seven humans. A committee of exactly 7 of these team members must be put together to work on bug testing. You may leave your answer unreduced. (a)How many committees can be chosen that contain exactly four robots and three humans? (b) How many committees can be chosen that contain at most two robots? (c) How many committees can be chosen that contain at least one human?