Question

An employer has $500 that she can award in bonuses to her 7 employees. If she wants all of the bonuses to be in $25 increments and not everyone has to receive bonuses, how many different ways are there for her to give out bonuses?

Answer 1

since 500 = 25*20 this is just the number of partitions of 20 into 7 parts
20 0 0 0 0 0 0 * 7!/6!
19 1 0 0 0 0 0 * 7!/5!
...
4 4 4 3 3 1 1 * 7!/3!2!2!
...
Finally, calculate the permutations of each partition