Final answer:
There are 5,040 different ways the letters of 'statistics' can be arranged.
Step-by-step explanation:
To find the number of different ways the letters of 'statistics' can be arranged, we need to calculate the number of permutations. In this case, the word 'statistics' has 10 letters, but the letter 's' appears twice, so we have to consider that. The formula to calculate permutations with repetition is P(n) = n! / (r1! * r2! * ... * rk!), where n is the total number of objects and r1, r2, ..., rk are the frequencies of each repeated object.
So, for the word 'statistics', we have:
P(10) = 10! / (3! * 3! * 2!)
Calculating this expression, we find that there are 5,040 different ways the letters of 'statistics' can be arranged.