Question:
A closet contains 10 pairs of shoes. What is the probability of getting a pair if two left and two right shoes are chosen?
I did it this way but I'm not sure if it's correct:
number of ways to select two left and two right shoes $=(10C2)\times(10C2) =45\times45 =2025$
number of ways to select a matching pair =N(select 1 pair from 10 and select both left and right, then select 2 pairs from remaining 9 and select 1 of right or left from each of pair)
$=(10C1)\times(2C2)\times(9C2)\times2 =10*1*36*2 =720$
therefore probability= $720/2025 =16/45$
Best Answer
I would say that given that you have 2 left shoes.
The chance that the first right shoe chosen does not pair with one of the two you have is $\frac {8}{10}$ and the second not pairing is $\frac{7}{9}$
No pair is $\frac {56}{90}.$
Pairing up at least once must be $\frac {34}{90} = \frac {17}{45}$