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6.Permutation and Combination
medium
In how many ways can $6$ persons be selected from $4$ officers and $8$ constables, if at least one officer is to be included
A
$224$
B
$672$
C
$896$
D
None of these
Solution
(c) Required number of ways
${ = ^4}{C_1}{ \times ^8}{C_5}{ + ^4}{C_2}{ \times ^8}{C_4}{ + ^4}{C_3}{ \times ^{8}}{C_3}{ + ^4}{C_4}{ \times ^8}{C_2}$
$ = 4 \times 56 + 6 \times 70 + 4 \times 56 + 1 \times 28 = 896$.
Standard 11
Mathematics
