Suppose that we have pn objects and we have p slots, how many ways can we distribute those pn objects on those p slots so that each slot has exactly n object?

basically the answer should be (pn)! /(n! ^p)

but i have been trying to prove this and i just can't,

since we are distributing pn objects on p slots (keep in mind that the slots are distinguishable but the position within the slots are not) we first need to chose a slot, and then put n objects in it, and do it for all p slots

which means the answer should be c(p,1)*c(pn, n)*c(p,2)*c(n(p-1))**c(p, p)*c(n,2n),i am not completely sure on this last one but if i simplify this last one i get (p! *(/(n! ^p) and that's wrong so where is my mistake?