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A group of 4 members is to be selected from 2 women, 2 elderly men, and 4 young men, subject to the conditions that the group must contain at least one woman, at least one elderly man, and no more than two young men. How many such groups can be formed?
- 40
- 41
- 16
- 32
Correct answer: 41
Solution
With 2 women, 2 elderly, 4 young, group of 4 needs >=1 woman, >=1 elderly, <=2 young. Cases (w,e,y): (1,1,2):2*2*6=24; (1,2,1):2*1*4=8; (2,1,1):1*2*4=8; (2,2,0):1*1*1=1; (1,3,..)/etc invalid. Total = 24+8+8+1 = 41.
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