How many 5-letter words are possible out of a 6-letter word? How many 5-letter strings are possible out of the 6-letter word APPLES?
Here my attempt: if the 5-letter string has just 1 P. Then we have 5! ways of getting such strings. If the 5-letter string has 2 P's, then there are 4 ways this can be done namely:

P, P, A, L, E 

P, P, A, L , S

P, P, A, E, S

P, P, L, E, S

Each of of the above 4 cases has: 5!/2! = 60 distinct 5-letter strings.
So the answer is : 120 + 4*60 = 360 such strings.
A generating function approach might work. It should be the exponent of $x^5$ in $$5! \left(1 + \frac{x}{1!}\right)^4 \left(1 + \frac{x}{1!} + \frac{x^2}{2!}\right)$$

This gives me 360.

Related: 6-letter permutations in MISSISSIPPI