There are 6 men and 8 women in a club. A comm | vedclass

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(D) Total number of people $= 6 + 8 = 14$.Total number of ways to select $5$ people out of $14$ is given by ${}^{14}C_{5} = \frac{14 	imes 13 	imes

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$1996$

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(D) Total number of people $= 6 + 8 = 14$.Total number of ways to select $5$ people out of $14$ is given by ${}^{14}C_{5} = \frac{14 	imes 13 	imes 12 	imes 11 	imes 10}{5 	imes 4 	imes 3 	imes 2 	imes 1} = 2002$.Number of ways such that no woman is selected means all $5$ people are selected from the $6$ men. This is given by ${}^{6}C_{5} = 6$.The number of ways to select at least one woman is equal to (Total ways) - (Ways with no women).Required number of ways $= 2002 - 6 = 1996$.

There are $6$ men and $8$ women in a club. $A$ committee of $5$ people has to be formed. What will be the number of ways to select $5$ people if at least one woman is selected?

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