SOLUTION: (a) The organizer of a television show must select 5 people to participate in the show. The participants will be selected from a list of 30 people who have written in to the show.

Question 1132167: (a) The organizer of a television show must select 5 people to participate in the show. The participants will be selected from a list of 30 people who have written in to the show. If the participants are selected randomly and none of the 30 people are the same age, what is the probability that the 5 youngest people will be selected?

(b) Evaluate the expression.
11C4

(c) There are 8 members on a board of directors. If they must form a subcommittee of 6 members, how many different subcommittees are possible?

Answer by ikleyn(52797) (Show Source): You can put this solution on YOUR website!
.

(a)  In all, there are   =  = 142506 different ways to select group of 5 persons from 30 persons.


     The group of 5 youngest persons of 30 is the UNIQUE such group of 5 persons from 30, under given conditions.


     So, the probability you are looking for is  .     ANSWER



(b)   = .

     Use your calculator.



(c)   =  = 28.     ANSWER

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All these problems/questions are about COMBINATIONS.

On Combinations, see the lessons
    - Introduction to Combinations
    - PROOF of the formula on the number of Combinations
    - Problems on Combinations
    - OVERVIEW of lessons on Permutations and Combinations
in this site.

Also, you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Combinatorics: Combinations and permutations".

Save the link to this textbook together with its description

Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson

into your archive and use when it is needed.

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