Six text books numbered 1, 2, 3, 4, 5 and 6 are arranges at random. What is the probability that the text books 2 and 3 will occupy consecutive places ?

Options

A. `1/2`
B. `1/3`
C. `1/4`
D. `1/6`

Answer

B

Explanation

Total number of possible arrangements n(s) = 6!.
Since 2 and 3 occupy consecutive places, so, they are grouped together.
So, there will be 5! such arrangements. But 2 and 3 can be arranged in themselves in 2! Ways
Required Probability `= (5! xx 2!)/(6!) = 2/6 = 1/3`