Question

In how many ways can one select 7 member committee from 10 distinct persons if only three persons qualify to be chairperson?

Answer 1

Answer on question #85652 – Math– Discrete Mathematics

Question

In how many ways can one select 7 member committee from 10 distinct persons if only three persons qualify to be chairperson?

Solution

One chairperson can be elected from three candidates in three ways. We have to choose 6 from the rest of 9 people. It can be done $C_9^6 = C_9^{9-6} = C_9^3 = \frac{9 \cdot 8 \cdot 7}{1 \cdot 2 \cdot 3} = 3 \cdot 4 \cdot 7 = 84$. Taking three opportunities of the choice of the chairperson into account, we have $3 \times 84 = 252$ ways.

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