The word MISSISSIPPI consists of 11 letters where the letter M appears 1 time, I appears 4 times, S appears 4 times, and P appears 2 times.
The formula for the number of different arrangements of letters in a word is given by:
\(\frac{n!}{n_1! \times n_2! \times \ldots \times n_k!}\)
where \(n\) is the total number of letters, and \(n_1, n_2, \ldots, n_k\) are the frequencies of the repeated letters.
For MISSISSIPPI:
\(n = 11, \quad n_1 = 4 \text{ (I)}, \quad n_2 = 4 \text{ (S)}, \quad n_3 = 2 \text{ (P)}\)
Substitute these values into the formula:
\(\frac{11!}{4! \times 4! \times 2!}\)
Calculate the factorials:
\(11! = 39916800, \quad 4! = 24, \quad 2! = 2\)
\(\frac{39916800}{24 \times 24 \times 2} = \frac{39916800}{1152} = 34650\)
Therefore, the number of different arrangements is 34650.
