Question

3 boys and 3 girls are to sit in a row. How many ways can this be done if all boys sit together

Answer 1

Three boys can sit together in ³P₃ ways. Now considering 3 boys as 1 group, 3 girls and 1 group of boys, i.e., altogether 4 can sit in ⁴P₄ ways.

Hence, the total number of seating arrangements in which all boys sit together

= ³P₃ × ⁴P₄

= 3!4!

= 3 × 2 × 1 × 4 × 3 × 2 × 1

= 144.