hi guys,
check out this problem.
The number of ways of selecting 10 balls from infinite number of green, red,black and white balls ?
the number of ways will be 4 multichoose 10
(3 + 10)! / (3!10!)
= 286
Could you please elaborate the solution?
Thanks
Thanks
could you follow my method if not reply me this is vijay
use multinomial theorem
(1+x+x2+x3...............)4
=(1-x)-4
now collect x10 coefficient from this
by (n+r-1) c r i.e (4+10-1) c (10)
= 13 c 3
=286
Hi,
Why cant we just say it as below?
Since there are infinite balls of each type, all of each type being identical, we can discard all other balls except 10 of each type. Thus, we have 40 balls in all. Our problem now translates into finding the no. of ways to select 10 of the 40 balls, with four identical gps. This is the same as saying,
Find the number of words that can be formed the letters GGGGGGGGGG, RRRRRRRRRR, BBBBBBBBBB and WWWWWWWWWW (ie 10 Rs, 10 Gs, 10W, and 10Bs) which is (40!)/10!30!(10!)^4
the problem can be easily solved using multinomial theorem.
i.e. the problem is equivalent to finding the number of solutions for the equation
a+b+c+d=10
sincethere are an infinite number of balls of each type writing a generating polynomial for each variable(as a gp) and multipying the answer should be the coefficient of 10 in
the expansion of (1-x)-4