the no. of ways of selecting 8 balls out of an infinite no. of white, red, yelow and brown balls is:

ans: ¹¹C₃

HI Basit,

Say we select x1 white balls, x2 red and x3 yello balls from the set of infinite balls.

Then x1+x2+x3=8 where each Xi ≥ 0.

The number of non-negative integral solutions of the eqn x1+x2+...xn = r is ^n+r-1C_r (This is dervided from Binomial Co-eff method).

So the solution of above eqn is ¹¹C₈ = ¹¹C₃.

Hope that helps.

Best Regards,

Ashiwn (IIT Madras).

X1+X2+X3+X4 = 8.

So ^8+4-1C₈ = ¹¹C₈.

Best Regards,

Ashwin (IIT Madras).

Hello , Ashwin 

  How there is ¹¹C₈=¹¹C₃   ( PLZ EXPLAIN IN BRIEF.........)

      THANKS!

Hi Basit,

That is because nCr = nCn-r

Which is one of the most importatn property of Combinatorics.... The Proof is quite easy.

Use the factorial notation, you will see nCr = n!/{r!(n-r)!}

and nCn-r = n!/{(n-r}!r!}..... Clearly both are same.

So 11C3 = 11C8.

Best Regards,

Ashwin (IIT Madtras).