Question
In how many ways can the letters of word ‘ASSASSINATION’ be arranged so that the arrangements be such that they start with O and end with T and the S’s are all together ?
Solution
Number of letters:
A → 3, S → 4
I → 2, N → 2
T → 1, O → 1
Total letters 13.
Tie the four S's.
Number of arrangements = 
...(i)
Mix with remaining to give:
[3 (A) + 2 (I) + 2 (N) + 1 (T) + 1 (O)] + 1 = 10
Fix O at first place.
Number of permutations = 
...(ii)
Fix T at the last place.
Number of permutations = 
...(iii)
Now, we have
3 (A) + 2 (I) + 2 (N) + 1 (four S's tied) = 8 letters
Number of arrangements = 
Hence, by fundamental principle of counting, the total number of permutations
= 1 x 1 x 1 x 1680 = 1680.
