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

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

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?

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:

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

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

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

## Answers ( )

Answer: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:[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

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

[tex]C_{100,14} = \frac{100!}{14!(86)!} = 44,186,943,000,000,000[/tex]

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