Question

5 players are to be selected from 8 . how many combination are possible?​

Answer 1

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

TO DETERMINE

The number of combination when 5 players are to be selected from 8

CONCEPT TO BE IMPLEMENTED

1. r number of objects can be selected from n objects in $\sf{\large{ {}^{n} C_r} \: \: ways}$

2.

$\displaystyle{\large{ {}^{n} C_r = \frac{n! }{r! \: (n - r)! } }}$

CALCULATION

Here total number of players = n = 8

Players to be selected = r = 5

Hence the total number of combinations

$= \displaystyle{\large{ {}^{8} C_5 }}$

$\displaystyle{ = \frac{8! }{5! \: 3! }}$

$\displaystyle{ = \frac{8 \times 7 \times 6}{3 \times 2} }$

$= 56$

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