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

A bag contains 12 pairs of socks. Four socks are picked up at random.

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

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

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