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Consider this Question

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

This question is answered in math.stackexchange.com.

Accepted answer is 12!/(5!. 4! . 3!)

Now see this question

Number of ways we can distribute 5 red balls, 5 white balls and 5 blue balls into 3 different boxes?

This question is answered in careerbless and answer is 21*21*21

One of the answer is wrong because both questions should follow the same approach. By looking into both answers, I am not able to identify which is right.

Can anyone can help me to find the right approach or to understnad why the same kind of question is interpreted in two different ways?

Thanks

Kiran
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    I assume the first question should read "$5$ " where it says $55$ and $12$ where it says $1212$? In any case, the problems are not the same. "Slots" can only take one ball each (hence, in this case, none can be empty). "Boxes" can take any number, or can be empty. – lulu Jan 31 '16 at 12:16
  • @lulu, thanks, that is the point, thanks a lot. I spent lot of time, but didn't figure out this. – Kiran Jan 31 '16 at 12:18

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