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

A. `8//15`
B. `1//5`
C. `2//15`
D. `4//15`

Answer

D

Explanation

Total number of ways in which 6 students can stand in row is 6!.
One student can stand between A and B in `.^(4)C_(1)xx2!` ways.
Considering these three as one individual we have 4 students who can stand in a row in 4! Ways.
Therefore, number of ways in which one student is there between A and B and is `.^(4)C_(1)xx2!xx4!`.
Hence, required probability `=(.^(4)C_(1)xx2!xx4!)/(6!)=(4)/(5)`