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A rack has 5 different pairs of shoes. The number of ways in w

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A rack has $5$ different pairs of shoes. The number of ways in which $4$ shoes can be chosen from it, so that there will be no complete pair is

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80

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Alexander Discussed

A rack has

5

different pairs of shoes. The number of ways in which

4

shoes can be chosen from it, so that there will be no complete pair is

6 mins ago

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Text solutionVerified

We need to select 4 different pair of shoes, so that we don't get a complete pair, that means we need to select 4 shoes from 5 choices.

\Rightarrow_{5} C_{4}

Now from selected pairs we can choose any one of the shoe of the pair

_{5} C_{4} (_{2} C_{1} \times_{2} C_{1} \times_{2} C_{1} \times_{2} C_{1}) = 5 \times 16 = 80

Hence,

(D)

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Question Text	A rack has $5$ different pairs of shoes. The number of ways in which $4$ shoes can be chosen from it, so that there will be no complete pair is
Answer Type	Text solution:1
Upvotes	150