IIT JEE , AIEEE Forum - Mathematics , Algebra - Ways of selecting 1 or more balls out of 10 white 9 green & 7 blue balls

dey_pras23

Ways of selecting 1 or more balls out of 10 white 9 green & 7 blue balls

RyuAmakusa

let a be the no. of white balls,b be the no. of green balls,and c be the no.of blue balls selected

then what we want is the no. of non negative integeral solns. for the eqn

a + b + c =i where

0

a

10

0

b

9

0

c

7 and i runs from 1 to 26 and it can be solved by multinomial theorm

deedee

can we do it in this way

{(2^9+10+7) -1}

deedee

is dat methdo rite??

akhil_o

the general method is
for p objects of one type, q of another type and so on...
ways to select one or more is
(p+1)(q+1)(r+1)....-1

so here
(10+1)(9+1)(7+1)-1
=879

Decoder

u want to take out the ball ..no matter wat the coluor is..or to say u shud not be empty handed..

here goes my funda..
u can take 10 white or no white.....11 options.
similarlrly.. 9 blue or no no blue 10 options..

and also 8 options for green..
this will give u any no. of balls..
but u want at least one..
so rule out tht option in wic u have no blue-no hwite-no green condition..tht case is only one..
so no.of options u now have is..
11*10*8 -1...

actually this is used to find divisors or factors of a given no..

Ask & Discuss Questions with Community & Experts