"how many distinct ways can the letters in tallahassee be arranged"

We can use permutation to solve for this problem. Permutation is used to determine the number of arrangements you can do with a given or fixed set. The word TALLAHASSEE has identical letters so we will use this formula:

      

where: n is the number of elements in the set
            n1 is the number of identical element (object 1)
            n2 is the number of identical element (object 2)
            n3 is the number of identical element (object 3)

So first let's see how many identical objects there are and the number of each.
A = 3        L= 2      S = 2      E= 2
How many elements in the set? 11
Now input your given:




= 831,600 arrangements

That they are numbers and related to each other.