Aspire Faculty ID #4319 · Topic: NIMCET 2017 · Just now
NIMCET 2017

From a group of 7 men and 6 women, a committee of 5 persons with more males than females is to be formed. In how many ways can this be done?

Solution

Possible cases:

  • (5M,0F): $^7C_5 \times ^6C_0$
  • (4M,1F): $^7C_4 \times ^6C_1$
  • (3M,2F): $^7C_3 \times ^6C_2$

Total = $^7C_5\times^6C_0 + ^7C_4\times^6C_1 + ^7C_3\times^6C_2 $ $= 21 + 210 + 525 = 756$

Answer: $\boxed{756}$ ✅

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