Let r and n be positive integers such that 1 ≤ r ≤ n. Then prove the following: n. n – 1 C r – 1 = (n – r + 1)( n C r – 1 )

Question

Philoid · Accepted Answer

Given that we need to prove n.^{n – 1}C_{r – 1} = (n – r + 1).ⁿC_{r – 1}

Consider L.H.S,

We know that

And also n! = n(n – 1)(n – 2)…………2.1

⇒

= R.H.S

∴ L.H.S = R.H.S, thus proved.