SOLUTION: A certain congressional committee consists of 12 senators and 14 representatives. How many ways can a subcommittee of 5 be formed if at least 4 of the members must be senators?

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Question 1097044: A certain congressional committee consists of 12 senators and 14 representatives. How many ways can a subcommittee of 5 be formed if at least 4 of the members must be senators?
Found 3 solutions by jorel1380, greenestamps, MathTherapy:
Answer by jorel1380(3719) About Me  (Show Source):
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12 choose 4=495
495 x 14=6930 different sub-committees possible
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Answer by greenestamps(13200) About Me  (Show Source):
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The first tutor who responded perhaps misread the problem. His answer is the number of ways that the committee can be formed with EXACTLY 4 senators, which means 1 of the 14 representatives:
C%2812%2C4%29%2AC%2814%2C1%29+=+495%2A14+=+6930

But the problem says the committee must have AT LEAST 4 senators. So the earlier answer is missing the number of ways in which all 5 committee members are senators:
C%2815%2C4%29+=+1365

So the final answer to the problem is
6930%2B1365+=+8295

Answer by MathTherapy(10552) About Me  (Show Source):
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A certain congressional committee consists of 12 senators and 14 representatives. How many ways can a subcommittee of 5 be formed if at least 4 of the members must be senators?
Choosing 4 senators from 12 senators, times choosing 1 rep, from 14 reps., PLUS Choosing 5 senators from 12 senators, times choosing 0 reps, from 14 reps. This is:  <======= Correct answer