`^404C_4-^303C_4.^4C_1+^202C_4.^4C_2-^101C_4.^4C_3=`

404C_(4)-^(303)C_(4)*^(4)C_(1)+^(202)C_(4)*^(4)C_(2)-^(101)C_(4)*^(4)C_(3)=

Show that ^10C_4=^9C_(4)+^9C_3

[(. ^nC_0+^n C_3+)-1/2(.^n C_1+^n C_2+^n C_4+^n C_5]^2 + 3/4(.^n C_1-^n C_2+^n C_4 +)^2= equals to a. 3 b. 4 c. 2 d. 1

Prove that : ^2C_1+ ^3C_1+ ^4C_1= "^3C_2+ ^4C_2 .

[(^nC_0+^n C_3+)-1/2(^n C_1+^n C_2+^n C_4+^n C_5]^2 + 3/4(^n C_1-^n C_2+^n C_4 +)^2= a. 3 b. 4 c. 2 d. 1

1. ^n C_0+4^1. ^n C_1+4^2. ^n C_2 + 4^3. ^n C_3+….+4^n. ^n C_n =

Find the coefficient of x^4 in the expansion of (1+x)^n (1-x)^n . Deduce that C_2=C_0C_4-C_1C_3+C_2C_2-C_3C_1+ C_4 C_0 .

If alpha=^m C_2,t h e n^(alpha)C_2 is equal to a. ^m+1C_4 b. ^m-1C_4 c. 3^(m+2)C_4 d. 3^(m+1)C_4