In how many ways can 15 distinct balls be distributed into f

In how many ways can 15 distinct balls be distributed into five distinct urns if each urn must contain at least one ball? Explain.

Solution

Answer:

Here both balls and boxes are different. Hence the order of selection is important.
Given that any box can contain more than one ball. Hence,

1^st ball can be placed into any of the 5 boxes
2^nd ball can be placed into any of the 5 boxes
3^rd ball can be placed into any of the 5 boxes
...
15^th ball can be placed into any of the 5 boxes

Hence, the required number of ways = 5 × 5 ... (15 times) = 5¹⁵