Find the value of `n!/r!(n-r)!` if `n=8` and` r=6`

Evaluate (n!)/(r!(n-r)!) , where n=15,r=4

Evaluate (n !)/(r !(n-r)!) , when n = 5, r = 2.

Evaluate : (n!)/((n-r)!) where n=5,r=2

If f(n)=sum_(r=1)^(n) r^(4) , then the value of sum_(r=1)^(n) r(n-r)^(3) is equal to

Find the value of (Sigma_(r=1)^(n) 1/r)/(Sigma_(r=1)^(n) k/((2n-2k+1)(2n-k+1))) .

If .^(n+1)C_(r+1):^(n)C_(r):^(n-1)C_(r-1)=11:6:3 , find the values of n and r.

If .^(n+1)C_(r+1.): ^nC_r: ^(n-1)C_(r-1)=11:6:3 find the values of n and r.

If .^(n)C_(r-1): .^(n)C_(r): .^(n)C_(r+1)=3:4:5 , find the values of n and r.

If A_r=|(1,r,2^r),(2,n,n^2),(n,(n(n+1))/2 ,2^(n+1))| , then the value of sum_(r=1)^n A_r is n (b) 2n (c) -2n (d) n^2

If a_(n) = sum_(r=0)^(n) (1)/(""^(n)C_(r)) , find the value of sum_(r=0)^(n) (r)/(""^(n)C_(r))