I have 10 identical pieces of candy. In how many different ways can I distribute the candies to 4 different kids?
Assuming that each kid got at least one piece of candy [ we don't want any riots....!!! ]
The number of ways is
C [ k -1 , n - 1 ]
Where = 10 and n = 4
So we have
C [ 9 , 3 ] = 84 ways
[ This is analogous to the problem of distributing k identical balls into n distinguishable boxes]