If there r 5 different colour balls , and 3 different boxes. in how many ways can the balls be placed in the boxes such that no box is empty?

Number of ways to fill the 3 boxes with one ball: 5P3.

Now we have to place the remaining 2 balls in the boxes.

One way of doing this is by placing one ball into one of the 3 boxes and the other ball in a different box. This can be done in: 3P2 ways.

The other option is to place both of the 2 balls into the same box. As there are 3 available boxes, number of possiblities is 3.

Thus total number of ways of acheiving the given task is:

5P3 x (3P2 + 3) = 540

 

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