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The number of ways such that 5 red, 4 yellow and 3 blue balls be arranged in a row if the balls of the same colour are indistinguishable is P, then find sum of digits of P.

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We have 3 types of balls (red, yellow and blue), so the number of arranging then is 3!. Now, the balls in each type can also be arranged in their own type.

since the balls are different

P = 3! x 5! x 4! x 3! 

= 6 x 120 x 24 x 6 

= 103680

Sum of digits of P is 1 + 0 + 3 + 6 + 8 + 0 = 18

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