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(52787)   (Show Source): You can put this solution on YOUR website!
.

The groups of 3 persons can be formed from 12 persons by   =  =  220 ways (helicopter committee).


The groups of 5 persons can be formed from 12 persons by   =  = 792  ways (Glider committee).


If no other restrictions, then these two committees can be formed by  . = 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   =  = 11*5 = 55.


For 5-member committees, the number of such committees is   =  = 330.


Therefore, the ANSWER  to the problem's question is


    . - . = 174240  - 55*330 = 147015 ways.


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