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

Question

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

Infinity Learn · Accepted Answer

The first distribution of $$4$$ left gloves to four persons in $$4$$! ways.    Now, no one gets the corresponding right $$glove=4$$!(1-11$$!$$+12$$!$$-13$$!$$+14$$!$$)                                                                                      $$=24(1-1+12-16+124)$$                                                                                      $$=9$$  Then, the number of favourable ways $$=$$ $$9$$·$$4$$! Total number of ways $$=4$$!·$$4$$!∴Required Probability $$=$$ $$2164$$!·$$4$$!$$=38=0.375$$

Introduction to probability

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$G i v e n f o u r p a i r o f g l o v e s, t h e y a r e d i s t r i b u t e d t o f o u r p e r s o n s .$
$E a c h p e r s o n i s g i v e n a r i g h t h a n d e d a n d l e f t h a n d e d g l o v e .$
$T h e p r o b a b i l i t y t h a t n o p e r s o n g e t s a p a i r i s e q u a l t o$

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Introduction to 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

The first distribution of 4 left gloves to four persons in 4! ways. Now, no one gets the corresponding right glove=4!(1-11!+12!-13!+14!) =24(1-1+12-16+124) =9 Then, the number of favourable ways = 9·4! Total number of ways =4!·4!∴Required Probability = 2164!·4!=38=0.375

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$G i v e n f o u r p a i r o f g l o v e s, t h e y a r e d i s t r i b u t e d t o f o u r p e r s o n s .$
$E a c h p e r s o n i s g i v e n a r i g h t h a n d e d a n d l e f t h a n d e d g l o v e .$
$T h e p r o b a b i l i t y t h a t n o p e r s o n g e t s a p a i r i s e q u a l t o$