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?

Mr.Owl
Oct 23, 2017

#1**+2 **

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 :

http://www.careerbless.com/aptitude/qa/permutations_combinations_imp7.php

CPhill
Oct 23, 2017