Question

The Number Of Ways Of Selecting 20 Objects Out Of 41 Objects Of Which 20 Are Identical And The Remaining 21 Are Distinct Is ___

Answer 1

Answer:

Given that, out of 41 objects 20 are identical and remaining 21 are distinct, so in following ways, we can choose 10 objects.

0 identical + 10 distincts, number of ways =1×21C10

1 identical + 9 distincts, number of ways =1×21C9

2 identicals + 8 distincts, number of ways =1×21C8

........

........

So, total number of ways in which we can choose 10 objects is

21C10+21C9+21C8+...+21C0=x(let) ...(i)

⇒21C11+21C12+21C13+...+21C21=x ...(ii)

[∵nCr=nCn−r]

On adding both Eqs. (i) and (ii) , we get

2x=21C0+21C1+21C2+...+21C10+21C11+21C12+...+21C21

⇒ 2x=221⇒ x=220