In how many ways can 15 identical math books be distributed to six students?

Question

question: In how many ways can 15 identical math books be distributed to six students? i try do this: P(15,6) could be this the answer or i should check the question, i find out other? help please

Answer 1

The problem is not solved by a permutation because the books are identical. This is a stars-and-bars problem, with $15$ stars (the books) and $5$ bars creating six spaces for the six different students. The answer is therefore $\binom{15+5}5=\binom{20}5$.

Answer 2

One particular distribution of the $15$ identical books to $6$ students could be

$$B B B | B B | B B B | B B | B B B | B B$$

Note that this has needed $5$ dividers, and these could be placed anywhere in the configuration of $15 + 5 = 20$ symbols. Thus the number of ways of distributing them = ${20}\choose 5$