Find the value of `4nC_0 + 4nC_4 + 4nC_8 + 4nC_12+...+4nC_(4n) `

Find the value of ^4nC_(0)+^(4n)C_(4)+^(4n)C_(8)+...+^(4n)C_(4n)

If .^nC_30=^nC_4 , find n

Find n if "^nC_12 = ^nC_8

Let a=(4^(1/401)-1) and let b_n = nC_1 + nC_2 . a+ nC_3. a^2+......+ nC_n .a^(n-1). Find the value of (b_2006 – b_2005)

If "^nC_10 = ^nC_5 find "^nC_14

The value of ""^0C_0-^nC_1+^nC_2-....+ -1^(n^n)C_n is

The value of 4(nC_(1)+4.nC_(2)+4^(2)*nC_(3)+......+4^(n-1)} is

If "^nC_5= ^nC_12 find n.

If (1+x)^(n)=nC_(0)+nC_(1)x+....+nC_(n)x^(n) where n is a positive integer,then find the value of nC_(0)+nC_(4)+nC_(8)+....