Question

A boy has 4 different boxes and 5 different marbles. In how many ways can he place the marbles in the boxes such that each box has at least one marble ?

Answer 1

Boxes  4 different       marbles  5  different 
(A,B,C,D)                   (1,2,3,4,5)

   Each box needs to get one marble at least.  The number of ways of arranging four marbles of 5 in four boxes = 5P4 = 5!.
 
  Then the 5th marble can be placed in any of the 4 boxes.

So total number of ways = 5!  * 4 = 480

Answer 2

Let the boxes be b 1, b 2, b 3 and b 4
so, 
box 1 can be filled in ways = 5
box 2 can be filled in ways = 4
box 3 can be filled in ways = 3
box 4 can be filled in ways = 2
so, 5*4*3*2 = 120 ways
Lastly any of 4 can be filled with 5th marble in 4 ways.
So, 120*4 = 480 ways  Answer