Question

Permutation:

Answer 1

Here one player cannot be repeated so repeating is not allowed.

• Hence we use combination here

• n=7
• r=5

Total ways

$\\ \rm\hookrightarrow ^nC_r=\dfrac{n!}{r!(n-r)!}$

• Put values

$\\ \rm\hookrightarrow ^7C_5$

$\\ \rm\hookrightarrow \dfrac{7!}{5!(7-5)!}$

$\\ \rm\hookrightarrow \dfrac{7!}{5!2!}$

$\\ \rm\hookrightarrow \dfrac{7\times 6\times 5!}{5!(2)}$

$\\ \rm\hookrightarrow \dfrac{7(6)}{2}$

$\\ \rm\hookrightarrow \dfrac{42}{2}$

$\\ \rm\hookrightarrow 21ways$

Answer 2

Formula for permutation is:

$\boxed{ \tt^{n} C_{r} = \frac{n!}{r!(n - r)!} }$

Calculation,

Plug in the values:

Required number of ways = ²C7

• n = 7
• r = 5

$\sf \frac{7!}{5!(7 - 5)!}$

$\sf \frac{7 \times 6 \times \cancel{5!}}{ \cancel{5! }\times 2!}$

$\sf \frac{7 \times 6 }{ 2!}$

$\sf \frac{42 }{ 2!}$

$\sf \frac{42 }{ 2} = 21$

Thus, The players can be selected in 21 different ways!!~