+51 1. How many ways are there to put 6 balls in 3 boxes if the balls are not distinguishable but the boxes are?
2. How many ways are there to put 5 balls in 3 boxes if the balls are not distinguishable and neither are the boxes?
+128406 Assuming that some boxes could remain empty.....
For the first one....let the number of balls = k and the number of boxes = n
So...we have
C( k + n - 1 , n - 1) = C( 6 + 3 - 1 , 3 - 1) = C (8, 2) = 28 ways
For the second one.....we have the following partitions of 5 indistinguishable balls in 3 indistinguishable boxes
5, 0, 0
4, 1, 0
3, 2, 0
3, 1, 1
2, 2, 1 = 5 ways
