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Question

# There are 20 pairs of shoes in a closet. Four shoes are selected at random. The probability that there is exactly one pair is

A
20c140c4
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B
20C1×(38C219)40C4
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C
20C1×38C240C4
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D
20C1×19C240C4
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Solution

## The correct option is D 20C1×(38C2−19)40C4Out of 20 pairs, we need to select 1 pair and the other 2 shoes should not form a pair. Thus, this can be achieved in: 201C∗(192C∗21C∗21C)(i.e. select one pair, then out of the remaining 19 pairs, select 2 pairs and from each pair select one shoe)We can also say that: select one pair, then out of the remaining 38 shoes, select 2 shoes and eliminate the 19 cases where these 2 shoes form a pair, i.e. 201C∗(382C−19)Therefore, probability =201C∗(382C−19)404C

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