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June 26th, 2017, 11:46 PM   #1
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How to calculate ways of putting 5 groups of balls into 6 places

Hi, I've run into a puzzle and haven't found a solution yet. hope someone can help me out. The problem is as below:

I have 5 groups of balls:
Group 0: 01 - 09
Group 1: 10 - 19
Group 2: 20 - 29
Group 3: 30 - 39
Group 4: 40 - 45
And I need to arrange these five groups of balls into 6 places. Order doesn't matter, repetition is allowed.

What formula should we use to calculate ways of putting 5 groups of balls into 6 places?

I arranged it manually and the result I found was 210, but I don't know how to calculate it. looking forward to your help. thank you.
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July 18th, 2017, 07:31 AM   #2
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I do not really understand the question but if order doesnt matter i would guess
P(n,k)=n!/(n-k)!
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July 18th, 2017, 09:17 AM   #3
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If I understand the question (a big if there) there are six ways to choose the place that does not get a group, right?

Let's call the five remaining places A, B, C, D, E.

There are five groups that could go in A, then four remaining, either of which could go in B, and three remaining that could go in C, and two remaining that could go in D, and only one left that could go in E.

So $6 * 5 * 4 * 3 * 2 * 1 = 720 = 6! $
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