Question

Find the number of ways of selecting a team of 3 boys and 2 girls from 6 boys and 4 girls.

Answer 1

Number of boys = 6
∴ Number of ways of selecting 3 boys = ⁶C₃
Number of girls = 4
∴ Number of ways of selecting 2 girls = ⁴C₂
Hence, the number of ways of selecting a team of 3 boys and 2 girls
= ⁶C₃ × ⁴C₂

= `(6!)/((6 - 3)!3!) xx (4!)/((4 - 2)!2!)`

= `(6!)/(3!3!) xx (4!)/(2!2!)`

= `(6 xx 5 xx 4 xx 3!)/((3 xx 2 xx 1)3!) xx (4 xx 3 xx 2!)/((2 xx 1)2!)`

= (5 × 4) x (2 × 3)
= (20) × (6)
= 120