Question

A supermarket offers icecream in $10$ differnt varieties.
Icecreams of each variety are identical in how many ways $4$ icecreams can be selected:
(i) without any restriction
(ii) Atleast $2$ ice creams of the same variety are taken

Answer 1

(i) Each of $4$ ice cream has $10$ choices, hence number of ways $={10}^4$

(ii) Choice of same variety ${=}^{10}{C}_1$ other $2$ ice cream has $10$ choice each

$\Rightarrow$ Total number of ways ${=}^{10}{C}_1\times {10}^2={10}^3$