Probability : A bag contains 12 pair socks . Four socks are picked up at random. Find the probability that there is at least one pair. Probability : A bag contains 12 pair socks . Four socks are picked up at random. Find the probability that there is at least one pair. 
My approach : 
Number of ways of selecting 4 socks from 24 socks is n(s) = $^{24}C_4$ 
The number of ways of selecting 4 socks from different pairs is n(E) = $^{12}C_4$
$$\Rightarrow P(E) = \frac{^{12}C_4 }{^{24}C_4}$$
Therefore, the probability of getting at least one pair is 
$$1- \frac{^{12}C_4 }{^{24}C_4}$$
But the answer is $$1- \frac{^{12}C_4 \times 2^4}{^{24}C_4}$$... Please guide the error .. thanks..

The error is in the second line.  The number of ways to select four different pairs must be multiplied by the number of ways to select just one sock from each of those four selected pairs. 
This is:  (12C4 × 24)
