IIT JEE , AIEEE Forum - Mathematics , Algebra

elastiboysai

Ya Das Rt

Your soln seems 2 be d same as mine wich is

LET THE COLOURS BE Ci (0<i<=6)

BALLS OF COLOUR Ci : 6-i (0<i<6)

Let the no. of selections from Ci be aj

a1+a2+a3+a4+a5+a6=6

0<=aj<=6-j (0<j<=6)

Using multinomial theorom we have to find the coefficient of a^6
in (a^0+a^1+..a^p) (6<=p<=1)

Using formula for GP we get
(1-a^7)(1-a^6)(1-a^5)(1-a^4)(1-a^3)(1-a^2)(1-a)^-6

Neglecting higher powers of a(>6), and then simplifying we get
it as coeff of a^6 in
(1-a^2-a^3-a^4)(1-a)^-6

Hence coefficient of a^6 = 6+6-1C6 - 6+4-1C4 - 6+3-1C3 -

6+2-1C2
=259

I don think ders any oder method??