How many ways can we put $5$ red balls, $4$ green balls and $3$ white balls into $12$ slots?

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How many ways can we put $5$ red balls, $4$ green balls and $3$ white balls into $12$ slots?

Would it be $12!$ or $\dfrac{12!}{5!4!3!}$? I'm confused here.

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Since (red/green/white) balls are indistinguishable from other (red/green/white) balls, the answer is $\dfrac{12!}{5!4!3!}$, not $12!$.