SOLUTION: Suppose that there are 55 democrats and 45 republicans in the U.S. Senate. A committee of seveen senators is to be formed by selecting members of the senate randomly. A) what is

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Question 345970: Suppose that there are 55 democrats and 45 republicans in the U.S. Senate.
A committee of seveen senators is to be formed by selecting members of the senate randomly.
A) what is the probability that the committee is composed of all democrats?
B) What is the probility the committe is composed of all republicans?
C) What is the probability that the committee is composed of three democrats and four republicans?
Answer by sudhanshu_kmr(1152) (Show Source):
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55 democrats and 45 republicans, we have to form committee of 7

no. of ways of selecting 7 from total 100 = 100C7

A.
no. of ways of selecting 7 democrats from 55 = 55C7

the probability that the committee is composed of all democrats= 55C7/ 100C7
..............................................................................

B.
no. of ways of selecting 7 republicans from 45 = 45C7
the probility the committe is composed of all republicans= 45C7 / 100C7

..............................................................................
C.
no. of ways of selecting 3 democrats from 55 and 4 republicans from 45
= 55C3 * 45C4
probability that the committee is composed of

three democrats and four republicans = (55C3 * 45C4) / 100C7

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