Find the number of ways of arranging 15 students `A_1,A_2,........A_15` in a row such that (i) `A_2`, must be seated after `A_1 and A_2`, must come after `A_2` (ii) neither `A_2` nor `A_3` seated brfore `A_1`

Options

A. `(2!xx15!)/(3!)`
B. `(15!)/(3!)`
C. `2!15!`
D. None of these

Answer

A

Explanation

`(a)` First arrange `12` persons `A_(4),A_(5),….A_(15)` in `"^(15)P_(12)` ways
There remains `3` places. Keep `A_(1)` in the first place and arrange `A_(2)`, `A_(3)` in the remaining two places in `2!` ways.
`:.` Required no. of arrangements `="^(15)P_(12).1.2!`