Question

Prove That: (permutations and combination)

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

Answer 1

Step-by-step explanation:

Sol : Take L.H.S (n - 1)p r + r (n- 1)p(r-1) ⇒ ( n - 1)! / ( n -1 - r)! + r × ( n - 1)! / ( n -1 - (r - 1))! ⇒ ( n - 1)! / ( n -1 - r)! + r × ( n - 1)! / ( n - r )! ⇒ ( n - 1)! / ( n - r -1)! + r × ( n - 1)! / ( n - r ) ( n - r -1)! ⇒ ( n - 1)! / ( n - r -1)! [ 1 + r / (n - r)] ⇒ ( n - 1)! / ( n - r -1)! [ (n - r + r) / (n - r)] ⇒ ( n - 1)! x(n) / ( n - r -1)! x (n - r) ⇒ n! / (n - r)! ∴ P( n , r) = L.H.S L.H.S = R.H.S.