Question

The principal would like to assemble a committee of 11 students from the the 19 member student council. How many different committees can be chosen?

Answer 1

Answer: 75582 different committees

Explanation

Given

• Committee: 11 students

,

• Member student council: 19 students

Procedure

As the order of choosing is not important, then we can use combinations:

$_nC_r=\frac{n!}{(n-r)!r!}$

where n is the number of items in a set and r is the number of items selected from the set. Applying the formula to our problem:

• n = ,19

,

• r = 11

Thus, replacing these values and simplifying:

$_{19}C_{11}=\frac{19!}{(19-11)!11!}$$_{19}C_{11}=\frac{19!}{(8)!11!}$$_{19}C_{11}=\frac{19!}{8!\cdot11!}$$_{19}C_{11}=75582$