Question

Prove that if r is less than or equal to s and s is less than or equal to n then p(n,s) is divisible by p(n,r)

Answer 1

Answer:

n! = n!

(n−r)!

∴(n−r)!=(n−s)!

Given r<s⟹−r>−s

∴(n−r)>(n−s)

We know that two different factorials are zero and one

∴n−r=1andn−s=0

∴r=n−1,s=n

∴r+s=2n−1