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

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(C) The total number of ways to select $6$ persons from $12$ ($4$ officers + $8$ constables) is $^{12}C_6 = \frac{12 	imes 11 	imes 10 	imes 9 	im

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$896$

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(C) The total number of ways to select $6$ persons from $12$ ($4$ officers + $8$ constables) is $^{12}C_6 = \frac{12 	imes 11 	imes 10 	imes 9 	imes 8 	imes 7}{6 	imes 5 	imes 4 	imes 3 	imes 2 	imes 1} = 924$.The number of ways to select $6$ persons such that no officer is included (i.e.,all $6$ are constables) is $^8C_6 = ^8C_2 = \frac{8 	imes 7}{2} = 28$.The number of ways to select at least one officer is (Total ways) - (Ways with no officer) = $924 - 28 = 896$.

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

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