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 $12$ (i.e.,$4$ officers + $8$ constables) is given by $^{12}C_6$.The number of ways to select

Vedclass · Accepted Answer

$896$

Vedclass · Answer

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

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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