1. ## Combination Question

Question:
Ten boxes each hold one white ball and one coloured ball every colour being different. Find the number of ways in which one ball may be taken from each box if half those taken are white.

10 boxes 10 choices 2 balls in each box but half of them already taken to be white
so there are 5 boxes left with 2 choices 5C2

so; 5 x 5C2 = 50
but the answer in the textbook is 252

2. ## Re: Combination Question

first pick the 5 boxes you will choose the white ball from.

There are $\dbinom{10}{5}=252$ of these

And that's all the choosing you can do. The other colors are just the ones left in the boxes you didn't choose.

3. ## Re: Combination Question

Originally Posted by bigmansouf
Question:
Ten boxes each hold one white ball and one coloured ball every colour being different. Find the number of ways in which one ball may be taken from each box if half those taken are white.

10 boxes 10 choices 2 balls in each box but half of them already taken to be white
so there are 5 boxes left with 2 choices 5C2

so; 5 x 5C2 = 50
but the answer in the textbook is 252