How many different committees can be formed from 11 teachers and 48 students if the committee consists of 2 teachers and 4 ​students?

Question

How many different committees can be formed from

1111

teachers and

4848

students if the committee consists of

22

teachers and

44

​students?

Answer 1

This problem involves the fundamental counting principle. If there are m ways to perform something, and n ways to perform something else, the number of ways to perform both is m times n.

How many ways can we get a set of 2 teachers out of 11? Since order does not matter this is a combination (11 things taken 2 at a time).

₁₁C₂ = 11(10)/2 = 55

How many ways to form a committee of 4 students out of 48?

₄₈C₄= [48(47)(46)(45)]/4!=194580

Applying the fundamental counting principle the number of possible committees is:

55(194580).= ?