A closet has 5 pairs of different types of shoes. How many ways 4 shoes can be drawn from the closet so that there will be no complete pair?

# A closet has 5 pairs of different types of shoes. How many ways 4 shoes can be drawn from the closet so that there will be no complete pair?

1. A
200
2. B
160
3. C
40
4. D
80

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### Solution:

Total shoes = 5 pairs of shoes
= Total ways of selecting 4 pair out of 5
Now for every pair, on selecting 1 shoe, this can be done in 1 pair out of 2 ways
Total number of ways
Hence, Option (4) is the correct answer.

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