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The number of words that can be formed u...

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

A

`11!//8`

B

`11!`

C

`"^(11)P_(6)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
`(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`
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