Q38,paper 2,d13. If n and r are non-negative integers and n ≥r, then p(n + 1, r) equals to

(A) p(n, r) (n + 1)/(n + 1 – r)

(B) p(n, r) (n + 1)/(n – 1 + r)

(C) p(n, r) (n – 1)/(n + 1 – r)

(D) p(n, r) (n + 1)/(n + 1 + r)

Answer A.

Explanation.

P(n+1,r)=(n+1)!/(n+1-r)!

(n+1)n!/((n+1-r)(n-r)!)=p(n,r)/(n+1-r)                                                                  

 where p(n,r)= n!/(n-r)!.