SOLUTION: . A committee of 5 is to be chosen from 12 members of the Board of Directors, 3 of whom are accountants. How many ways can this done if at least two of the committee members must b

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Question 945069: . A committee of 5 is to be chosen from 12 members of the Board of Directors, 3 of whom are accountants. How many ways can this done if at least two of the committee members must be accountant?
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
. A committee of 5 is to be chosen from 12 members of the Board of Directors, 3 of whom are accountants. How many ways can this done if at least two of the committee members must be accountant?
1. We calculate the number of committees of 5 without regard for the restriction
   of the accountants.
2. We calculate the number of committees with no accountants.
3. We calculate the number of committees with only 1 accountant.
4. We subtract the results of 2 and 3 from the result of 1.

1. 12 members choose 5 = 12C5.
   That's 792
2. 9 non-accountants choose 3 = 9C5
   That's 126
3. 3 accountants choose 1 = 3C1 = 3
   9 non-accountants choose 4 = 9C4 = 126
   That's 3*126 = 378
4. 792-126-378 = 288   

Edwin
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