From a group of 10 men and 8 women the no. of ways of forming a committee of 8 members with not more than 5 men and not less than 5 women’s

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answer is 8061.

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Detailed Solution

From group of 10 men and 8 women committee of 8 members with not more than 5 men and not less than 5 women is formed in the following ways

Case i If 3 men and 5women we selected number of ways $^{10} C_{3} \times^{8} C_{5} = 6720$

Case ii If 2 men and 6 women are selected number of ways $^{10} C_{2} \times^{8} C_{6} = 1260$

Case iii If 1 man and 7 women are selected numbers of ways $^{10} C_{1} \times^{8} C_{7} = 80$

Case iv If 0 men and 8 women are selected numbers of ways $^{10} C_{0} \times^{8} C_{8} = 1$

Total number of ways is 6720+1260+80+1=8061

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