SOLUTION: four shoes are taken at ramdom from five different pairs .whait is the probability that there is at least one pair among them?

Question 1068363: four shoes are taken at ramdom from five different pairs .whait is the probability that there is at least one pair among them?
Answer by addingup(3677) (Show Source): You can put this solution on YOUR website!
The number of ways to choose 4 out of 10 shoes is
Choose 1st shoe out of 10
Choose 2nd shoe out of 9
Choose 3rd shoe out of 8
Choose 4th shoe out of 7
:
The number of ways to choose 4 out of 10 shoes with no pairs is:
Choose the 1st shoe out of 10
Choose the 2nd shoe out of 8
Choose the 3rd shoe out of 6
Choose the 4th shoe out of 4
So the probability of choosing 4 out of 10 shoes with at least one pair is:
1−10⋅8⋅6⋅4/10⋅9⋅8⋅7 = 1-0.381 = 0.62 or 62%
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