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.

Question

Filo · Accepted Answer

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 balls6C3​×5C3​×5C3​=3!3!6!​×3!2!5!​×3!2!5!​                                =3!×3×2×16×5×4×3!​×3!×2×15×4×3!​×3!×2×15×4×3!​                               =20×10×10                               =2000

Question Text	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.
Answer Type	Text solution:1
Upvotes	153

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.

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