In how many ways can we select a committee of five persons from a group of five women and sixmen if:i) there is no restriction.ii) exactly 2 men in the committee.i) at least four women are in the committee.

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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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2. An emergency committee consisting of 12 health's officer staffs is chosen from 10 doctors and 12 nurses. Calculate the number of ways the committee is made up of: a. 5 doctors and 7 nurses. b. not more than 6 doctors. c. at least 3 doctors and 4 nurses.
A volleyball team consists of 14 players: There are 6 rookies and the rest of the players are veterans. a) In how many ways can they select a group of 4 to play a sand volleyball game if exactly three of the players must be rookies. b) In how many ways can they select a group of 4 to play a sand volleyball game if at least three of the players must be rookies.
9.) There are 347 NCAA teams today. a.) How many ways can there be to get the top 10 winners? b.) How many ways are there to pick the teams to play in a 16 team bracket tournament?
6. A jar is to be filled with 100 jelly beans. There are five varieties of beans to choose fromn and we are required to use between 10 and 50 beans of each variety. How many different ways of filling the jar are there?
Six teachers and 12 students volunteer for a committee to discuss extra-curricular activities. How many committees of 5 people can be made if: a) there must be 3 students on the committee b) there must be no more than 2 teachers on the committee c) there must be at least one teacher and at least one student on the committee d) Barry and Miss Morrison cannot be on the committee together.
A committee of six is to be made from 4 students and 8 teachers. In how many ways can this be done: i. If the committee contains exactly four teachers ii. If the committee contains at most four teachers
How many committees could be formed from 10 students if. a) there must be at least 8 people? b) there are 5 people on the committee but Joey and Sally must be selected?
A class contaions 10 girls and 10 boys. how many 3 person committee can be formed that will give the boys a majority?
In a UC student club, a president and treasurer are to be chosen consisting of 45 people. a. How many different choices of officers are possible if there are no restrictions? b. How many different choices of officers are possible if A will serve only if he is president? c. How many different choices of officers are possible if B and C will serve together or not at all. d. How many different choices of officers are possible if D and E will not serve together?
2. How many ways are there to place 12 people into four groups of equal size?

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In how many ways can we select a committee of five persons from a group of five women and six men if: i) there is no restriction. ii) exactly 2 men in the committee. ii) at least four women are in the committee.