Question

Seven persons are to be seated in a row.The probability that two particular persons sit next to each other is

Answer 1

The required probability P(E) = $\dfrac{2}{7}$

Step-by-step explanation:

The number of ways in which seven persons are seated in a row = 7!

Two persons sitting next to each other = 6!

To find, the probability that two particular persons sit next to each other = ?

Let E be the event of  the two particular persons sit next to each other.

∴ P(E) = $\dfrac{Number of favourable outcomes}{Total number of possible outcomes}$

= $\dfrac{6!}{7!}\times 2!$

= $\dfrac{6!}{7 \times 6!}\times 1 \times 2$

= $\dfrac{2}{7}$

Thus, the required probability P(E) = $\dfrac{2}{7}$