# Thread: Permutation and combination help!

1. ## Permutation and combination help!

A box contain 8 balls, of which 3 are identical and the other 5 are different from each other. 3 balls are to be picked out of the box; the order in which they are picked out does not matter. Find the number of different possible selections of 3 balls. can someone solve this question asap? thanks!

2. Originally Posted by CautionItsHot
A box contain 8 balls, of which 3 are identical and the other 5 are different from each other. 3 balls are to be picked out of the box; the order in which they are picked out does not matter. Find the number of different possible selections of 3 balls. can someone solve this question asap? thanks!
What have you tried so far? Please take the time to familiarize yourself with some basic forum rules. This is not a place to get people to do your homework for you.

http://www.mathhelpforum.com/math-he...ng-151422.html

That said, rather than finding a more elegant solution that generalizes to harder problems, for this we can simply break down into cases. Suppose the 3 identical balls are identified by the colour green. Four cases: 0 green, ... , 3 green. Then you've reduced it to problems that (supposedly) you already know how to solve.

3. case 1: 0 green 3diff =5C3
case 2: 1 green 2 diff=5C2x3C1
case 3:2 green 1 diff= 5C1x3C2
case4: 3 green 0 diff=3C3

Thats wat i done intinially. i add them up and my ans is 56. but the correct ans is 26. where is it that i have gone wrong

4. Originally Posted by CautionItsHot
case 1: 0 green 3diff =5C3
case 2: 1 green 2 diff=5C2x3C1
case 3:2 green 1 diff= 5C1x3C2
case4: 3 green 0 diff=3C3

Thats wat i done intinially. i add them up and my ans is 56. but the correct ans is 26. where is it that i have gone wrong
You are treating the green balls as distinguishable. Note that C(8,3) = 56.

Corrected work: C(5,0) + C(5,1) + C(5,2) + C(5,3) = 26.