SOLUTION: How many different committees can be formed from 9 teachers and 33 students if the committee consists of 2 teachers and 2 ​students?

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Question 1170164: How many different committees can be formed from 9 teachers and 33 students if the committee consists of 2 teachers and 2 ​students?

Answer by ikleyn(52778) About Me  (Show Source):
You can put this solution on YOUR website!
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You select 2 teachers from 9 teachers in  C%5B9%5D%5E2 = %289%2A8%29%2F2 = 36 ways.


You select 2 students from 33 teachers in  C%5B33%5D%5E2 = %2833%2A32%29%2F2 = 528 ways.


These selections in different categories are independent - - - THEREFORE, the total number of all possible different selections

is the product  36*528 = 19008.     ANSWER

Solved.

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This problem is on  COMBINATIONS.

On Combinations,  see introductory lessons
    - Introduction to Combinations
    - PROOF of the formula on the number of Combinations
    - Problems on Combinations
    - Fundamental counting principle problems
    - 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.