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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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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.

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Solution

Required number of ways = 

\[{}^6 C_3 \times^5 C_3 \times^5 C_3 = \frac{6!}{3! 3!} \times \frac{5!}{3! 2!} \times \frac{5!}{3! 2!} = 2000\]
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Chapter 17: Combinations - Exercise 17.2 [Page 16]

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R.D. Sharma Mathematics [English] Class 11
Chapter 17 Combinations
Exercise 17.2 | Q 25 | Page 16

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