A bag contains 12 pairs of socks. Four socks are picked up at random. Find the probability that there is at least one pair.

Answer

`1-(.^(12)C_(4)xx 2^(4))/(.^(24)C_(4))`

Explanation

The 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)xx2^(4)`
`implies P(E) = (.^(12)C_(4) xx 2^(4))/(.^(24)C_(4))`
Hence, the probability of getting at least one pair is
`1 -(.^(12)C_(4) cc 2^(4))/(.^(24)C_(4))`