How many ways are there to put 5 balls in 3 boxes if the balls are not distinguishable but the boxes are?
That is the question but I have been trying it and getting many different answers, can someone help?
As Melody says.....take my answers at your own peril, Mr. Owl
If we have no restictions, the number of ways is given by
C ( k + n - 1, n - 1) here k is the number of balls and n is the number of boxes
C ( 5 + 3 - 1 , 3 - 1)
C ( 7, 2) = 21 ways
If we have to have at least one ball in each box
C ( k - 1, n - 1)
C ( 5 - 1 , 3 - 1 )
C ( 4, 2) = 6 ways
BTW ......here's a website that will help you with these type of problems :