Question

There are 11 shirts to select from in a store.

How many ways can 5 different shirts be selected?

PLEASE HELP

Answer 1

Given:

Total number of shirts to select from in a store = 11

To find:

How many ways can 5 different shirts be selected?

Solution:

Number of to select r items from n items is:

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

Total number of ways to select 5 different shirts from 11 shirts is:

$^{11}C_5=\dfrac{11!}{5!(11-5)!}$

$^{11}C_5=\dfrac{11\times 10\times 9\times 8\times 7\times 6!}{5\times 4\times 3\times 2\times 1\times 6!}$

$^{11}C_5=\dfrac{11\times 10\times 9\times 8\times 7}{5\times 4\times 3\times 2\times 1}$

$^{11}C_5=462$

Therefore, there are 462 ways to select 5 different shirts.