Question

In how many ways can a cricket team of eleven be chosen out of a batch of 15 players if there is no restriction on the selection?

Answer 1

$\blue{\huge{ \sf \fbox{ \: Solution : \: \: }}}$

11 players can be selected from 15 players in $\mathtt{ \fbox{ {}^{15}C_{11}}}$

Therefore ,

$\sf \hookrightarrow Total \: number \: of \: ways = {}^{15}C_{11} \\ \\ \sf \hookrightarrow Total \: number \: of \: ways = \frac{15!}{11!(15 - 11)!} \\ \\ \sf \hookrightarrow Total \: number \: of \: ways = \frac{15!}{11! \times 4!} \\ \\ \sf \hookrightarrow Total \: number \: of \: ways = \frac{15 \times 14 \times 13 \times 12 \times \cancel{11!}}{ \cancel{11!} \times 4!} \\ \\ \sf \hookrightarrow Total \: number \: of \: ways = \frac{15 \times \cancel{14 }\times 13 \times \cancel{12}}{ \cancel4 \times 3 \times \cancel2 \times 1} \\ \\ \sf \hookrightarrow Total \: number \: of \: ways = \frac{15 \times 7 \times 13 \times \cancel3}{ \cancel3} \\ \\ \sf \hookrightarrow Total \: number \: of \: ways = 15 \times 7 \times 13 \\ \\ \sf \hookrightarrow Total \: number \: of \: ways = 1365$

Hence , the number of permutations is 1365

Answer 2

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