SOLUTION: The composition of the Senate of the 107 Congress is 49 Republicans, 1 Independent and 50 Democrats. A new committee is being formed to study ways to benefit the arts in education

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Question 411150: The composition of the Senate of the 107 Congress is 49 Republicans, 1 Independent and 50 Democrats. A new committee is being formed to study ways to
benefit the arts in education.If 3 Senators are selected at random to head the committee,what is the probability that there will be one from each party, including the Independent?
Please let me know the process for figuring out this problem, as well as the soluition. Thank you!
Answer by sudhanshu_kmr(1152) About Me  (Show Source):
You can put this solution on YOUR website!

no. of ways to select 3 senators from total 100 = 100C3 = 161700 i.e n(S)

no. of ways to select 1 senators from each party = 50C1 * 49C1 * 1C1 = 2450
i.e n(A)

probability that one senator from each party P(A) = n(A)/n(S)
= 2450 /161700
=0.0151515..