Question

In how many ways can a team of 5 players be selected from 8 players so as not to include a particular player?
1. 42
2. 35
3. 21
4. 20

Answer 1

Correct Answer - Option 3 : 21

Concept:

Combination Formula

ⁿC_r = \(\rm \frac{n!}{r! (n - r)!}\)

Calculation:

A particular player should not be included 

We have to select 5 players from (8 - 1) = 7 players.

⇒  required number of ways =  ⁷C₅

\(⇒ \frac{7!}{5! (7-5)!}\) = 21

∴ The required number of ways is 21.