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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

Monjur Alahi

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`
B. `63300`
C. `63260`
D. `63060`


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1 Answers

Salim Ahmed Kawsar

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Correct Answer - A
`(a)` Selecting any two pairs, number of ways `=.^(12)C_(2)`
Now we have to select remaining three shoes from `10` pairs such that no pair is selected.
Three shoes from different pairs can be selected in `.^(10)C_(3)xx2^(3)` (selecting three pairs and then from each pair selecting on shoe in `2` ways)
`:.` Total number of ways `=.^(12)C_(2)xx^(10)C_(3)xx2^(3)`

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