kim has 5 pairs of shoes; each pair is a different color...

Question

Kim has 5 pairs of shoes; each pair is a different color. If Kim randomly select 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

The OA is C.

I don't understand why that is the correct answer, I'm a little bit confused.

The first time that she select any shoes, the probability should be 2/10? I'm confused. Then in the second time that she select any shoes the probability should be 1/9? I'm not sure.

Experts, I need your help with this PS question. Thanks.

Brent@GMATPrepNow · Answer

AAPL wrote:Kim has 5 pairs of shoes; each pair is a different color. If Kim randomly select 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 techniques

P(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 pair
There are 5 different colors.
So, there are 5 different ways to get a matching pair

TOTAL number of ways to select 2 shoes
There 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 = 45

Aside: If anyone is interested, we have a video on calculating combinations (like 10C2) in your head: [url] https://www.gmatprepnow.com/module/gmat- ... /video/789

So, P(matching pair) = (5)/(45)
= 1/9
= C

Cheers,
Brent

Brent@GMATPrepNow · Answer

AAPL wrote:Kim has 5 pairs of shoes; each pair is a different color. If Kim randomly select 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 techniques

P(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 pair
There are 5 different colors.
So, there are 5 different ways to get a matching pair

TOTAL number of ways to select 2 shoes
There 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 = 45

Aside: If anyone is interested, we have a video on calculating combinations (like 10C2) in your head: [url] https://www.gmatprepnow.com/module/gmat- ... /video/789

So, P(matching pair) = (5)/(45)
= 1/9
= C

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

Scott@TargetTestPrep · Answer

AAPL wrote:Kim has 5 pairs of shoes; each pair is a different color. If Kim randomly select 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 techniques

P(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 pair
There are 5 different colors.
So, there are 5 different ways to get a matching pair

TOTAL number of ways to select 2 shoes
There 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 = 45

Aside: If anyone is interested, we have a video on calculating combinations (like 10C2) in your head: [url] https://www.gmatprepnow.com/module/gmat- ... /video/789

So, P(matching pair) = (5)/(45)
= 1/9
= C

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

Choose how you want to prepare

Get Ready for GMAT Test Day Faster with Live Online Classes

Target Test Prep EA OnDemand

Target Test Prep GMAT OnDemand

kim has 5 pairs of shoes; each pair is a different color...

GMAT/MBA Expert