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Number of ways in which the letters of t...

Number of ways in which the letters of the word 'ABBCABBC' can be arranged such that the word ABBC does not appear is any word is

A

`256`

B

`391`

C

`361`

D

`498`

Text Solution

Verified by Experts

The correct Answer is:
C
`(c )` `A's=2`, `B's=4`, `C's=2`
Total words formed `=(8!)/(4!2!2!)=420` ……..`(i)`
Let `ABBC='xx'`
Number of ways in which `xxABBC` can be arranged `=(5!)/(2!)=60`
But this includes `xxABBC` and `ABBCxx`.
The word `ABBCABBC` is counted twice in `60`m hence it should be `59`.
Hence, required number of ways `=420-59=361`
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