## U.S. Senate Committee has 14 members. Assuming party affiliation is not a factor in selection, how many different committees are possible fr

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?

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3 months 2022-02-12T05:16:22+00:00 1 Answer 0 views 0

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

Step-by-step 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.

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

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

$$C_{100,14} = \frac{100!}{14!(86)!} = 44,186,943,000,000,000$$

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