Question

Thad 21 different toys when I was little, and my mom asked me

to give 5 of my toys to my younger brother. In how many ways
can I choose the 5 toys?

Answer 1

20349.

Explanation:

It is given that,

Total number of toys = 21

Number of toys to be selected = 5

Total number of ways to select 5 toys from 21 toys is

`\text{Total ways}=^(21)C_5=(21!)/(5!(21-5)!)`

`=(21!)/(5!(21-5)!)`

`=(21\cdot 20\cdot 19\cdot 18\cdot 17\cdot 16!)/(5\cdot 4\cdot 3\cdot 2\cdot 1\cdot 16!)`

`=20349`

Therefore, the required ways are 20349.