Just for wiki's sake 2

Relevant wiki: Binomial Theorem

The formula to calculate a binomial coefficient $\binom{n}{k}$ is

$\binom{n}{k}=\frac{n!}{k!(n-k)!}. \ _\square$ .

Plug in our values, we get

$\binom{9}{2} + \binom{8}{3}$ = $\frac{9!}{2!(9-2)!} + \frac{8!}{3!(8-3)!}$ = $\frac{9!}{2!7!} +\frac{8!}{3!5!}$ = $36+56$ = $92$

Click here for help on computing factorials.

C(9,2) can be written as (9/2) (8/1) = 36; and C(8,3) can be written as (8/3) (7/2)*(6/1) = 56

Therefore sum is = 36+56 = 92

Case 1: n=9,k=2 . we want to choose 2 things out of 9, so two is selected others or not. i.e. S ,S ,NS ,NS ,NS ,NS ,NS ,NS ,NS . Therefore, (n items)! / (selected items)! * (non-selected items)! = 9! / 2!7! =36.

case 2: n=8,k=3 . As usual like case 1 ,so three is selected from eight others or not. i.e. S ,S ,S ,NS ,NS ,NS ,NS ,NS . Therefore, 8! (n items ) / 3! ( selected items) * 5! (non-selected items) = 56.

Sum of case 1 and case 2 :- 36+56 = 92

9C2=36 8C3=56 Ans. is (36+56)=92

refer wiki link for more details 1st step-find out both the binomial coefficients separately. 1st coefficient after applying formula gives 9!/2!7! which becomes 36 by calculation. 2nd coefficient gives 8!/3!5! after applying formula&it becomes 56. Last step -add both results(36+56)to get the result=96 Feel free to share any doubt.