Question

The congressional committees on mathematics and computer science are made up of five representatives each, and a congressional rule is that the two committees must be disjoint. If there are 385 members of congress, how many ways could the committees be selected?

Answer 1

Answer:

The committes can be selected in $1.752507297 \times 10^{19}$ ways

Step-by-step explanation:

The order in which the members are chosen to the committee is not important. So we use the combinations formula to solve this question.

Combinations formula:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

The two committees must be disjoint.

This means that a person cannot be part of both committes.

If there are 385 members of congress, how many ways could the committees be selected?

Since the committes are disjoint, 5(math) + 5(computer science) = 10 people will be chosen from the set of 385. So

$C_{385,10} = \frac{385!}{10!(385-10)!} = 1.752507297 \times 10^{19}$

The committes can be selected in $1.752507297 \times 10^{19}$ ways