Question

If six students, including two particular students A and B, stand in a row, then the probability that A and B are separated with one student in between them is ______.

Options

• `8/15`

• `4/15`

• `2/15`

• `1/15`

Answer 1

If six students, including two particular students A and B, stand in a row, then the probability that A and B are separated with one student in between them is `underlinebb(4/15)`.

Explanation:

Consider a group of three students A, B and another student in between A and B. Choice for a student between A and B is 4. A and B can interchange their places in the group in 2 ways.

Now the group of three students (student A, student B and a student in betWeen A and B) and the remaining 3 students can stand in a row in 4! ways.

Hence total number of ways to stand in a row such that A and B are separated with one student in between them = 4 × 2 × 4!

Now total number of ways to stand is 6 students stand in a row without any restriction = 6!

Hence required probability

= `(4 xx 2 xx 4!)/(6!)`

= `(4 xx 2)/(6 xx 5)`

= `4/15`