11I got this
b+c+d+e+b+c+d+e+f+g+h+i=n=2(b+c+d+e)+f+g+h+i+j
So number of solutions is co-efficient of xn in (x+x2+x3+...)5(x2+x4+x6.....)4.
All I did after this was to reduce this to GP form, but then got stuck.
In how many ways can n identical balls be distributed to nine persons A,B,C,D,E, F,G,H, I so that the number of balls recieved by A is the same as the total number of balls recieved by B,C,D,E together?
As of yet, I haven't been able to evaluate it in a closed form....getting it in terms of a summation, so need help.
-
UP 0 DOWN 0 0 4
4 Answers
62\sum{C^n_r\times C^n_r\times4^r\times4^{n-2r}}=\sum{C^n_r\times C^n_r\times4^{n-r}}
Even I cant think of something directly!
1162The previous answer was for n distinct object.. here they are similiar... so it becomes
\sum{^{r+3}C_3\times^{n-2r}C_3}
11SIR, MULTINOMIAL SE KUCH HOGA?
Can we end up with anything from what I've started with? [46]