# 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:

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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 : $\dfrac{2}{5}$

Concept:

The formula of the probability of an event is:

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

Calculation:

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

$\rm \frac{48}{120}$

$\dfrac{2}{5}$

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