How many words can be formed with the letters of the word 'LAHORE', if
(i) L and A are always together?
(ii) L and A are never together?

Explanation

In the word 'LAHORE'
No. of letters = 6
No. of ways to fill 6 places with 6 letters `= .^(6)P_(6) = lfloor6 = 720`
(i) If L and A are always together, treating them as one letter, then no of letters `= 6 - 2 +1 = 5`
No. of ways to fill 5 letters `= .^(5)P_(5) = 120`
No. of ways to arrange L and A at two places `= .^(2)P_(2) = lfloor2 = 2`
From multiplication rule
Required words `= 120 xx 2 = 240`
(ii) If L and A are never together then
Required words = Total words - No. of words in which L and A are always together `= 720 - 240 = 480`