# Balls matching boxes question

#### Usagi

##### Member
Hi guys, really simple question but...

I'm not quite sure on how they ended up with the expression for P(exactly one match). I would have done it in a more straight forward way, simply define A: matching the colour red in the red box only. B: matching the colour blue in the blue box only and C: matching the colour white in the white box only.

So P(exactly one match) = P(A)+P(B)+P(C) = $$\frac{3}{6} = \frac{1}{2}$$

How exactly did they get their expression?

Thanks

MHB Math Scholar