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Combination of r Things from n Things When All Are Not Different

There are 12 ...

Question

There are 12 pairs of shoes in a box. Then the possible number of ways of picking 7 shoes so that there are exactly two pairs of shoes are

A

63360

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B

63300

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C

63260

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D

63060

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Solution

The correct option is A 63360
Total number of ways of picking up 7 shoes with 2 pairs is $^{12} C_{2} \times^{10} C_{3} \times 2^{3}$

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