Bunuel wrote:

aadikamagic wrote:

A certain ski shop sells pairs of gloves in 12 different colors. If one pair of each color is dropped in a bag and a store clerk reaches in to draw two individual gloves simultaneously and at random, what is the probability that she draws two gloves of the same color?

A. 1/144

B. 1/143

C. 1/24

D. 1/23

E. 1/12

We have 2*12 = 24 gloves on the floor. After we pick ANY, there are 23 left and there is only 1 matching pair left for the one we've already picked, so P = 1/23.

Answer: D.

Or: there are 12 matching pairs, and \(C^2_{24}=23*12\) ways to pick any two. P = (favorable)/(total) = 12/(23*12) = 1/23.

Answer: D.

Hope it's clear.

Hi Bunuel,

why is (24c1 * 1) / 24c2 wrong??

As there are 24 gloves, we need to first pick one glove, so 24c1.

Then we have only one way to pick the other glove, so 1.

Total outcomes=picking two out of 24 = 24c2.

we get 2/23, so where am I going wrong?

Thanks,

Uma