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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?
Solution
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
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