The number of words that can be formed using all the letters of the word REGULATIONS such that `G` must come after `R`, `L` must come after `A`, and `S` must come after `N` are

Options

A. `11!//8`
B. `11!`
C. `"^(11)P_(6)`
D. none of these

Answer

A

Explanation

`(a)` The other five letters (other than `G`, `R`, `L`, `A`, `S`, `N`) in `11` places can be arranged in `"^(11)P_(5)` ways.
Then three remains six places.
Choose two of them in `"^(6)C_(2)` ways. In these places we can put `G`, `R` only `(i)` one way.
Similarly others.
`:.` Required no. of ways `="^(11)P_(5)xx^(6)C_(2)xx^(4)C_(2)xx^(2)C_(2)=11!//8`