SOLUTION: How many color arrangements are possible by placing 3 red balls, 5 green balls, and 2 yellow balls in a row?

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Question 1149052: How many color arrangements are possible by placing 3 red balls, 5 green balls, and 2 yellow balls in a row?

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
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Since the question asks about color arrangements, it means that except the color, the balls are considered as indistinguishable.



Then the formula and the answer are


    number of color arrangements = %283%2B5%2B2%29%21%2F%283%21%2A5%21%2A2%21%29 = 10%21%2F%283%21%2A5%21%2A2%21%29 =  = 25210.



The factorials in the denominator of the basic formula 

    number of color arrangements = {{10!/(3!*5!*2!)}}}

are associated with MULTIPLICITIES of repeating objects.