`sum_(r=0)^(20).^(50-r)C_6`

if sum_(r=0)^(25).^(50)C_(r)(.^(50-r)C_(25-r))=k(.^(50)C_25), then k equals: (a) 2^(25) (b) 2^(25)-1 (c) 2^(24) (d) 25^(2)

Coefficient of x^(48) in sum_(r=0)^(50)""^(50)C_(r).(x-2)^(x).3^(50-r) is

The value of sum_(r=0)^(50)(.^(100)C_(r).^(200)C_(150+r)) is equal to

Find the sum of the series sum_(r=0)^(50)(""^(100-r)C_(25))/(100-r)

The number of divisiors of the number (sum_(r=10)^(20)5^(r-1)19C_(r-1))/(sum_(r=0)^(17)17C_(r)4^(17.26)r) is equal to

sum_(r=0)^(10) r.^(10)C_(r),3^(r).(-2)^(10-r) is -

Evaluate .^(20)C_(5)+sum_(r=2)^(5).^(25-r)C_(4)