Combinations and Permutations - C(n+2,n)

Question

I need to express my result as a polynomial, we were given formulas which states the answers however I cannot find the formulas for these last 2

 

A) C(n+2,n)

 

C) C(C(n,k),(n¦(n-k)))    (the |n-k is below the n)

 

I just need help or a link to the formula of how to solve these 

Answer 1

In general, the formula for _nC_r is n! in the numerator, and r!(n-r)! in the denominator.

 

I take it that C(n+2,n) is just an alternative notation for _(n+2)C_n

 

A)    All you have to do is substitute:  you get numerator  (n+2)! which is (n+2)(n+1)(n!)

and then in the denominator you get n!(2)! and thus the final value is

½(n+2)(n+1).