In how many ways can 6 persons be selected fr | vedclass

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(C) Total number of persons to be selected is $6$ from $4$ officers and $8$ constables.To include at least one officer,we can use the complement metho

Vedclass · Accepted Answer

$896$

Vedclass · Answer

(C) Total number of persons to be selected is $6$ from $4$ officers and $8$ constables.To include at least one officer,we can use the complement method: Total ways - Ways with no officers.Total ways to select $6$ persons from $12$ $(4+8)$ is $\binom{12}{6} = \frac{12 	imes 11 	imes 10 	imes 9 	imes 8 	imes 7}{6 	imes 5 	imes 4 	imes 3 	imes 2 	imes 1} = 924$.Ways to select $6$ persons with no officers (i.e.,all $6$ are constables) is $\binom{8}{6} = \binom{8}{2} = \frac{8 	imes 7}{2} = 28$.Number of ways with at least one officer = $924 - 28 = 896$.

In how many ways can $6$ persons be selected from $4$ officers and $8$ constables such that at least one officer is included?

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