Maharashtra State BoardHSC Commerce 11th
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Find the number of ways of selecting a team of 3 boys and 2 girls from 6 boys and 4 girls. - Mathematics and Statistics

Sum

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

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Solution

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

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APPEARS IN

Balbharati Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board
Chapter 6 Permutations and Combinations
Exercise 6.6 | Q 8 | Page 89
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