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Question
Find the number of ways of selecting 9 balls from 6 red balls, 5 white balls and 5 blue balls if each selection consists of 3 balls of each colour.
Solution
There are a total of 6 red balls, 5 white balls, and 5 blue balls.
9 balls have to be selected in such a way that each selection consists of 3 balls of each colour.
Here,
3 balls can be selected from 6 red balls in 6C3 ways.
3 balls can be selected from 5 white balls in 5C3 ways.
3 balls can be selected from 5 blue balls in 5C3 ways.
Thus, by multiplication principle, required number of ways of selecting 9 balls
= 6C3 x 5C3 x 5C3 = `(6!)/(3!3!) xx (5!)/(3!2!) xx (5!)/(3!2!)`
= `(6 xx 5 xx 4 xx 3!)/(3! xx 3 xx 2) xx (5 xx 4 xx 3!)/(3! xx 2 xx 1) xx (5 xx 4 xx 3!)/ (3! xx 2 xx 1`
= 20 x 10 x 10
= 2000
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