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How many ways are there to put 5 balls in 3 boxes if the balls are distinguishable but the boxes are not?

 Jan 19, 2023
 #1
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This can be calculated using the formula for the number of ways to distribute n distinguishable objects into r indistinguishable boxes, which is: n+r-1 choose r. In this case, n = 5 and r = 3, so the formula becomes: 5+3-1 choose 3 = 7 choose 3 = 35.

 Jan 19, 2023
 #2
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Balls are DISTINCT and boxes are IDENTICAL:

 

sumfor(k, 0, 3, (5 nCr k)) ==26 - with no restrictions.

 

Source:  https://en.wikipedia.org/wiki/Twelvefold_way

 

{See the table at the very bottom of the page - item # 1]

 Jan 19, 2023
 #3
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sorry you are wrong

Guest Jan 20, 2023

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