SOLUTION: In how many ways can a committee of 5 senators be selected from the 100 members of the U.S. Senate so that no two committee members are from the same state?

Question 360140: In how many ways can a committee of 5 senators be selected from the 100 members of the U.S. Senate so that no two committee members are from the same state?
Answer by sudhanshu_kmr(1152) (Show Source): You can put this solution on YOUR website!

As there are 50 states and 2 senators from each states, total 100.
according to question, from each state at most 1 senator can be selected.

so, firstly we choose 5 states from which we have to select senators.

no. of ways to choose 5 states from total 50 states = 50C5

now, from each state we can choose senator in 2 ways.

total no. of ways to choose 5 senator from given 5 particular states = 2^5 = 32

so, total no. of ways to select 5 senators = 50C5 * 32
= 2118760 * 32
= 67800320

ANSWER IS: 67800320.

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Best of luck.......

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