SOLUTION: The Aviation Club at Rocco's school has 12 members (including Rocco). They need to choose a 3 person helicopter committee and a 4 person Glider Committee. Students can serve on eit

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Question 1150832: The Aviation Club at Rocco's school has 12 members (including Rocco). They need to choose a 3 person helicopter committee and a 4 person Glider Committee. Students can serve on either or both committees, but Rocco refuses to serve on both- he will only serve on one or the other. In how many ways can both committees be chosen?
Found 2 solutions by ikleyn, Alan3354:
Answer by ikleyn(52786) About Me  (Show Source):
You can put this solution on YOUR website!
.

The groups of 3 persons can be formed from 12 persons by  C%5B12%5D%5E3 = %2812%2A11%2A10%29%2F%281%2A2%2A3%29 =  220 ways (helicopter committee).


The groups of 5 persons can be formed from 12 persons by  C%5B12%5D%5E5 = %2812%2A11%2A10%2A9%2A8%29%2F%281%2A2%2A3%2A4%2A5%29 = 792  ways (Glider committee).


If no other restrictions, then these two committees can be formed by  C%5B12%5D%5E3.C%5B12%5D%5E5 = 220*792 = 174240 ways.


From this number, we must subtract the number of 3-member committees and 5-member committees that contain Rocco as one common members.


For 3-member committees, the number of such committees is  C%5B11%5D%5E2 = %2811%2A10%29%2F2 = 11*5 = 55.


For 5-member committees, the number of such committees is  C%5B11%5D%5E4 = %2811%2A10%2A9%2A8%29%2F%281%2A2%2A3%2A4%29 = 330.


Therefore, the ANSWER  to the problem's question is


    C%5B12%5D%5E3.C%5B12%5D%5E5 - C%5B11%5D%5E2.C%5B11%5D%5E4 = 174240  - 55*330 = 147015 ways.


Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Helicopters are dangerous. Don't go.
Trust me.