Problem Solving

uptowngirl92 wrote: Numerator:
Out of 20 shoes we have to select one shoe first..w/o any restrictions.So that's 20C1 (choosing one out of 20).
Now,the second show has to be the matching shoe.There is only ONE such possible shoe,so the probability of choosing that shoe is 1.

Denominator:
Chosing 2 shoes out of 20.So, 20C2

20C1/20C2 = 2/19

please explain:(

Jaspreet's solution above is the one I use for similar problems - it's very fast. Still, it's perfectly possible to solve as you've done above, provided you are consistent in how you count the numerator and denominator. In your solution above, when you count the number of selections for the numerator, you are assuming that order matters (you have a 'first shoe' and a 'second shoe'), but when you count the number of selections for the denominator, you are assuming that order does *not* matter - 20C2 means 'the number of ways to choose 2 things from 20 if the order is *not* important'.

It doesn't matter which perspective you take - you can think of selecting a first shoe, then a second, so order matters, or you can think of selecting both shoes at once, so order doesn't matter, but you must be absolutely sure you count the numerator and denominator in the same way: if you assume order matters when working out the numerator, you must assume it matters when you work out the denominator. So, if you assume order matters, you get, as you found above, 20 for the numerator, and 20*19 for the denominator (20 choices for the first shoe, 19 for the second). If you assume order does not matter, then there are 10 pairs we could choose that give the result we want, and 20C2 ways to choose two shoes. In either case, if you divide you'll get the answer: 20/(20*19) = 10/20C2 = 1/19.