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Five persons A, B, C, D and E occupy seats in a row at random. The probability that A and B sit next to each other is:
1. \(\dfrac{1}{4}\)
2. \(\dfrac{1}{2}\)
3. \(\dfrac{2}{5}\)
4. \(\dfrac{1}{3}\)

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Correct Answer - Option 3 : \(\dfrac{2}{5}\)


The formula of the probability of an event is:

P(A) = \(\rm \frac{Number of favourable outcomes}{Total number of favourable outcomes}\)


Total number of ways A, B, C, D and E can sit together = 5! = 120

Number of ways in which A and B sit together 

lets stick A and B together and treat them as 1 unit let us name this unit as U now

we have UCDE

number of ways of arranging this is 4!

but number of ways of arranging U is 2!

so total number of ways are 4!*2! = 4 \(\times\) 3  \(\times\) 2 \(\times \) 1 \(\times\) 2 = 48

The probability that A and B sit next to each other is

\(\rm \frac{48}{120}\)


Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur

Probability always lies from 0 to 1

The sum of probability of all possible outcomes is always 1



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