Question

How many ways can a team of 3 boys,2 girls and 1 transgender be selected from 5 boys, 4 girls and 2 transgenders?

Answer 1

Number of boys = 5

Number of girls = 4

Number of transgender = 2

Number of ways of selecting 3 boys from 5 boys = 5c₃

Number of ways of selecting 2 girls from 4 girls = 4C₂

Number of ways of selecting one transgender from 2 transgenders = 2C₁

Total number of ways of selection

= ⁵C₃ × ⁴C₂ × ²C₁ 

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

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

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

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

= 5 × 4 × 2 × 3

= 120