Question

In how many ways $18$ different objects can be divided into $7$ groups such that four groups contains $3$ objects each and three groups contains $2$ objects each.

Answer 1

Here total different objects are $n=18$

Four groups contains $3$ objects so ${}^{18}{C}_3$

Three groups contains $2$ objects so ${}^{18}{C}_2$

Hence No of ways $=\frac{18!}{({}^{18}{C}_3{)}^4({}^{18}{C}_2{)}^3}$