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A scientific committee is to be formed from 6 Indians and 8 foreigners, which includes at least 2 Indians and double the number of foreigners as Indians. Then the number of ways, the committee can be formed, is:
- 1625
- 575
- 560
- 1050
Correct answer: 1625
Solution
Cases with foreigners = 2x Indians: I=2,F=4 -> C(6,2)*C(8,4)=15*70=1050; I=3,F=6 -> C(6,3)*C(8,6)=20*28=560; I=4,F=8 -> C(6,4)*C(8,8)=15*1=15. Total = 1050+560+15 = 1625.
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