Probability of no matching pairs of shoes There are 3 different pairs ( i.e. 6 units say aa, bb, cc) of shoes in a lot. Now three person come and pick the shoes randomly (each get 2 units). Let p be the probability that no one is able to wear shoes (i.e. no one gets a correct pair) , then the value of $\frac{13p}{4-p}$ is?

The probability for the first person to pick a bad pair is $\frac 45$ (only one out of five shoes is a good second pick).
After this there is one valid pair left. The probability that the person to pick the left shoe of this pair also picks the right shoe, is $\frac 13$. Hence $p=\frac45\cdot\frac23=\frac{8}{15}$. I hope you can figure out the rest.
