Theorems of probability

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Given four pair of gloves, they are distributed to four persons. Each person is given a right handed and left handed glove, the probability that no person gets a pair is equal to

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Solution

Let first distribute 4 left gloves to four person in 4! ways. Now no one gets the corresponding right glove
$= 4! (1 - \frac{1}{1!} + \frac{1}{2!} - \frac{1}{3!} + \frac{1}{4!}) = 9$
$Then number of favorable ways = 9 \times 4! = 218$
$Total number of ways 4! \times 4!$
$∴ Required probability = \frac{216}{4! \times 4!} = \frac{216}{576} = \frac{3}{8}$

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Theorems of probability

Remember concepts with our Masterclasses.

Given four pair of gloves, they are distributed to four persons. Each person is given a right handed and left handed glove, the probability that no person gets a pair is equal to

Let first distribute 4 left gloves to four person in 4! ways. Now no one gets the corresponding right glove =4!1−11!+12!−13!+14!=9 Then number of favorable ways =9×4!=218 Total number of ways 4!×4!∴ Required probability =2164!×4!=216576=38

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