Carcass wrote:
Kim has 5 pairs of shoes; each pair is a different color. If Kim randomly selects 2 shoes without replacement from the 10 shoes, what is the probability that she will select 2 shoes of the same color?
(A) 2/5
(B) 1/5
(C) 1/9
(D) 1/10
(E) 1/25
Here's an approach that uses
counting techniquesP(matching pair) = (
number of ways to get a matching pair)/(
TOTAL number of ways to select 2 shoes)
number of ways to get a matching pairThere are 5 different colors.
So, there are
5 different ways to get a matching pair
TOTAL number of ways to select 2 shoesThere are 10 shoes altogether.
Since the order in which we select the 2 shoes does not matter, we can use combinations.
We can select 2 shoes from 10 shoes in 10C2 ways
10C2 =
45Aside: If anyone is interested, we have a video on calculating combinations (like 10C2) in your head. (see below)
So, P(matching pair) =
5/
45= 1/9
= C