A committee of 4 members is to be formed from | vedclass

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(D) We need to choose $4$ people out of $8$ ($4$ husbands and $4$ wives) such that no couple is selected.Let the couples be $(H_1, W_1), (H_2, W_2), (

Vedclass · Accepted Answer

$16$

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(D) We need to choose $4$ people out of $8$ ($4$ husbands and $4$ wives) such that no couple is selected.Let the couples be $(H_1, W_1), (H_2, W_2), (H_3, W_3), (H_4, W_4)$.First,we select $4$ couples out of $4$ from which we will pick one person each. This can be done in $^4C_4 = 1$ way.From each of the $4$ selected couples,we can choose either the husband or the wife. This gives $2^4$ ways.Total number of ways $= ^4C_4 	imes 2^4 = 1 	imes 16 = 16$.

$A$ committee of $4$ members is to be formed from $4$ couples (husbands and wives). In how many ways can the committee be formed such that no couple is included in the committee?

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