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

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    2022-02-12T05:18:08+00:00

    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.

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45:7+7-4:2-5:5*4+35:2 =? ( )