Question-85228

Question Number 85228 by mathocean1 last updated on 20/Mar/20

Commented by mathocean1 last updated on 20/Mar/20

p l e a s e h e l p m e \dots

Commented by abdomathmax last updated on 20/Mar/20

C_{n}^{p} - C_{n - 1}^{p} = \frac{n!}{p! (n - p)!} - \frac{(n - 1)!}{p! (n - p - 1)!}

= \frac{n (n - 1)!}{p (p - 1)! (n - p)!} - \frac{(n - 1)! (n - p)}{p (p - 1)! (n - p)!}

= \frac{(n - 1)!}{(p - 1)! (n - p)!} {\frac{n}{p} - \frac{n - p}{p}}

= \frac{(n - 1)!}{(p - 1)! (n - p)!} \times 1

= C_{n - 1}^{p - 1} \Rightarrow C_{n}^{p} = C_{n - 1}^{p} + C_{n - 1}^{p - 1}