Question

Write the number of ways in which 12 boys may be divided into three groups of 4 boys each.

Answer 1

Number of groups in which 12 boys are to be divided = 3
Now, 4 boys can be chosen out of 12 boys in\[\left( C_4 \times^8 C_4 \times^4 {C^{12}}_4 \right)\] ways.
These groups can be arranged in 3! ways. 
∴ Total number of ways =\[\frac{{}^{12} C_4 \times {}^8 C_4 \times {}^4 C_4}{3!} = \frac{12! \times 8!}{4! \times 8! \times 4! \times 4! \times 3!} = \frac{12!}{\left( 4! \right)^3 \times 3!}\]