no of ways in selecting 2 shoes from 10 shoes is =10c2=45ways

total no of pairs given =5

kim must choose from this 5 pairs so he will get shoes of same colour no of ways will be =5 ways

probability= 5/45 = 1/9

answer will be C

"if you like the explanation please press kudos please"

A very simple solution to a seemingly difficult problem without requiring to go in depths of the permutation.
5 pair of shoes = 10 shoes
Now it doesn't matter what shoe you select first as it's inconsequential. We only have to match 2nd pair so first pair can be a shoe of any color (if that's how 5 pairs are distinguished)

Hence the first probability is selecting any of 10 shoes from the 10 shoes = 10/10 = 1

Secondly, we need to select a shoe that matches the first shoe => this can only happen in 1/9 ways (because we have 9 shoes remaining and only 1 will complete the pair)

so by chain rule = 1* 1/9 = 1/9 (answer)

Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.