Question

The total number of ways in which 5 balls of different colours can be distributed among 3 persons so that each persons get at least one ball is?

Answer 1

the answer is 150 ways.......

Answer 2

i found the answer but i duno why.

Answer 3

number of ways=3*(5C3*2C1*1C1 + 5C2*3C2*1C1) = 150
5C3*2C1*1C1 means 1 person got 3 balls, the other 2 got 1 ball. 5C2*3C2*1C1 means 1 person got 2 balls, the other got 2 balls and the last 1 got 1 ball. Multiply by 3 is because there are 3 possibilities, either A, B or C guy.

Answer 4

sorry I can't help my eng is not good enough T T

Answer 5

dud nt understand

Answer 6

no prob plzz give ur best

Answer 7

i wiil try to understand utmost..

Answer 8

but I got 3*(C4,2 * 5 + C4,3*2) = 150

Answer 9

can u explain a little more

Answer 10

either method is correct. actually i think they are the same reasoning

Answer 11

*C5,3

Answer 12

@satellite73 then let you explain lol...

Answer 13

Lets assume the 3 people as A, B and C. 1st case : A get 3 balls, both B and C get 1 ball. for this case, number of ways = 5C3*2C1*1C1= 20. which means that among 5 balls, choose 3 for A, then among the remaining 2 balls choose 1 for B, remaining 1 ball for C. And since it can be either A or B or C gets 3 balls. so total number of ways for this case= 20x 3=60

2nd case : A gets 2 balls, B gets 2 balls, C gets 1 ball. number of ways = 5C2*3C2*1C1=30. which means that among 5 balls, choose 2 for A ; among the remaining 3 balls choose 2 for B, and remaining 1 ball for C. also the same thing it can be A B get 2 balls, A C get 2 balls, B C get 2 balls. so total number of ways = 3x30=90

So summarize for both cases total number of ways= 90 + 60 = 150

Answer 14

couldn't do better that glgan. very clear