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(C) Total number of members available $= 12$.Number of members to be selected $= 6$.Since a particular member must always be excluded,we effectively h

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$462$

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(C) Total number of members available $= 12$.Number of members to be selected $= 6$.Since a particular member must always be excluded,we effectively have to choose $6$ members from the remaining $(12 - 1) = 11$ members.The number of ways to select $6$ members from $11$ is given by the combination formula ${}^{n}C_{r} = \frac{n!}{r!(n-r)!}$.Substituting the values,we get ${}^{11}C_{6} = \frac{11!}{6!(11-6)!} = \frac{11!}{6! 	imes 5!}$.${}^{11}C_{6} = \frac{11 	imes 10 	imes 9 	imes 8 	imes 7 	imes 6!}{6! 	imes (5 	imes 4 	imes 3 	imes 2 	imes 1)} = \frac{11 	imes 10 	imes 9 	imes 8 	imes 7}{120} = 462$.Thus,the total number of ways is $462$.

There are $6$ members to be selected for a group to be sent abroad from a total of $12$ members. In how many ways can the selection be made such that a particular member is always excluded?

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