Question

U.S. Senate Committee has 14 members. Assuming party affiliation is not a factor in selection, how many different committees are possible from the 100 U.S. senators?

Answer 1

There are 44,186,943,000,000,000 different committees are possible from the 100 U.S. senators.

Explanation:

The order is not important.

Suppose the committee had two members.

Senator A and Senator B would be the same committee as Senator B and Senator A.

So we use the combinations formula to solve this problem

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) = (n!)/(x!(n-x)!)`

U.S. Senate Committee has 14 members. Assuming party affiliation is not a factor in selection, how many different committees are possible from the 100 U.S. senators?

This is the number of combinations of 14 from 100. So

`C_(100,14) = (100!)/(14!(86)!) = 44,186,943,000,000,000`

There are 44,186,943,000,000,000 different committees are possible from the 100 U.S. senators.