In how many ways a team of 11 must be selected from 5 men and 11 women such…
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In how many ways a team of 11 must be selected from 5 men and 11 women such that the team must comprise of not more than 3 men?
- A.
2009
- B.
2250
- C.
2256
- D.
2789
Attempted by 307 students.
Show answer & explanation
Correct answer: C
Answer: 2256
Count teams with 0, 1, 2, and 3 men separately, then sum the counts.
0 men and 11 women: C(5,0) × C(11,11) = 1 × 1 = 1
1 man and 10 women: C(5,1) × C(11,10) = 5 × 11 = 55
2 men and 9 women: C(5,2) × C(11,9) = 10 × 55 = 550
3 men and 8 women: C(5,3) × C(11,8) = 10 × 165 = 1650
Total = 1 + 55 + 550 + 1650 = 2256.