If Sigma(r=0)^(25) { ""^(50)Cr.""^(50-r...

If `Sigma_(r=0)^(25) { ""^(50)C_r.""^(50-r)C_(25-r)}=K(""^(50)C_(25))` then K is equal to

A

`2^(25)-1`

B

`(25)^2`

C

`2^(25)`

D

`2^(24)`

Verified by Experts

The correct Answer is:

C

Similar Questions

Explore conceptually related problems

if .^(2n)C_(2):^(n)C_(2)=9:2 and .^(n)C_(r)=10 , then r is equal to

f(n)=sum_(r=1)^(n) [r^(2)(""^(n)C_(r)-""^(n)C_(r-1))+(2r+1)(""^(n)C_(r ))] , then

If .^(15)C_(3r)=.^(15)C_(r+3), find .^(r)C_(2) .

((n),(r)) = (""^(n)P_(r))/(K), then K = ......

Let z_(r),r=1,2,3,...,50 be the roots of the equation sum_(r=0)^(50)(z)^(r)=0 . If sum_(r=1)^(50)1/(z_(r)-1)=-5lambda , then lambda equals to

sum_(r=0)^(n).^(n)C_(r)4^(r)=..........

""^(n)C_(n-r)+3.""^(n)C_(n-r+1)+3.""^(n)C_(n-r+2)+""^(n)C_(n-r+3)=""^(x)C_(r)

Evaluate ^(47)C_(4)+sum_(j=0)^(3)""^(50-j)C_(3)+sum_(k=0)^(5) ""^(56-k)C_(53-k) .

If {:((n),(r)):}=(n!)/(k), then K =.......

The sum of the series sum_(r=0)^(10) .^(20)C_(r) , is 2^(19)+{(.^(20)C_(10))/2} .