SOLUTION: In how many ways can a committee consisting of 2 faculty members and 5 students be formed if there are only 11 faculty members and 12 students eligible to serve on the committee?

Question 1089768: In how many ways can a committee consisting of 2 faculty members and 5 students be formed if there are only 11 faculty members and 12 students eligible to serve on the committee?
Answer by ikleyn(52835) (Show Source): You can put this solution on YOUR website!
.
Let us solve more simple problems first:

1.  In how many ways can you select 2 members among 11 faculty members?

    Since the order is not important, there are  =  = 55 ways.


2.  In how many ways can you select 5 students among 12 students?

    Since the order is not important, there are  =  = 792 ways.


3.  Now, the selections among these two groups are independent.
    Hence, in all , you have 55*792 ways in your global problem.

These magic numbers are called the numbers of combinations of n things taken k at a time.

About combinations and about these numbers, 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".

Do not forget to send your thanks.

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