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Question 1120045: There are 2 Senators from each of 50 states. We wish to make a 3-Senator committee in which no two members are from the same state.
a. How many ways can we choose 3 states to be represented?
b. How many ways can we choose a Senator from a chosen state?
c. How many ways can the 3-Senator committee be formed such that no 2 Senators are from the same state?
i solved a: 19,600. i just need help with b & c
Answer by ikleyn(52799)   (Show Source):
You can put this solution on YOUR website! .
(a) You correctly found 19600 for (a). Congratulations !
(b) To answer question (b), simply read the condition and the question ATTENTIVELY.
(c) You just found that 3 states can be selected by 19600 ways.
Next, for each of the selected 3 states we can choose one senator in 2 ways from the first of the 3 states;
in 2 independent ways from the second of the 3 states;
and in 2 independent ways from the third of the 3 states.
Hence, the answer to question (c) is 2*2*2*19600 = 156800 ways.
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