Question

3 boys and 3 girls are to sit in a row. How many ways can this be done if there is a girl at each end

Answer 1

The two ends can be occupied by 3 girls in ³P₂ ways.

After this the remaining 4 persons can sit at remaining 4 places in ⁴P₄ ways. 

Hence, the total number of seating arrangements

= ³P₂ × ⁴P₄

= `(3!)/(1!) xx 4!`

= 3 × 2 × 1 × 4 × 3 × 2 × 1

= 144.