1. In the word ASSASSINATION there are 13 letters, of which A appears 3 times, S appears 4 times, N appears 2 times, I appears 2 times and the rest all are different. Therefore the total number of ways is \(\frac{13 !}{3! \times 4 ! \times 2 ! \times 2 !}\) = 10810800.
2. 4 S’s are kept together and should be counted as one unit, then there are 10 units. The number of ways is \(\frac{10 !}{3! \times 2 ! \times 2 !}\) = 151200.
3. Number of words in which 4S’s do not come together = Total number of words – 4S’s together = 10810800 -151200 = 10659600.
4. The word will start with any one of the 4 A’s. Then total letter arrange will be 12. Number of words in which begin with A \(\frac{12 !}{2! \times 4 ! \times 2 ! \times 2 !}\) = 2494800.
