In 13 cricket players 4 are bowlers, then how many ways can form a cricket team of 11 players in whi

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6.Permutation and Combination

medium

In the $13$ cricket players $4$ are bowlers, then how many ways can form a cricket team of $11$ players in which at least $2$ bowlers included

A

$55$

B

$72$

C

$78$

D

None of these

Solution

(c) The number of ways can be given as follows

$2$ bowlers and $9$ other players ${ = ^4}{C_2}{ \times ^9}{C_9}$

$3$ bowlers and $8$ other players ${ = ^4}{C_3}{ \times ^9}{C_8}$

$4$ bowlers and $7$ other players ${ = ^4}{C_4}{ \times ^9}{C_7}$

Hence required number of ways

$ = 6 \times 1 + 4 \times 9 + 1 \times 36 = 78$.

Standard 11

Mathematics

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