How many words can be formed with the letters of the word 'PENCIL' in which
(i) 'C' and 'L' are always together?
(ii) 'C' comes just after 'L'?

Explanation

No. of letters in the word 'PENCIL' = 6
(i) If C and L. are always together, then treating them as one letter,
No. of letter `= 6 - 2 +1 = 5`
No. of ways to fill 5 places from these 5 letters `= .^(5)P_(5) = lfloor5 = 120`
No. of arrangement of C and L: placing at two positions
`=.^(2)P_(2) = lfloor2 = 2`
From multiplication theorem
Required arrangement `= 120 xx 2 = 240`.
(ii) If C comes just afer L, then they will be placed in order L and C as one letter
No. of letters `= 6 - 2 +1 = 5`
No. of arrangement of 5 letters, placing at 5 positions
`= .^(5)P_(5) = lfloor5 = 120`
`:.` Required arrangement = 120.