How many ways can the letters in Toronto be arranged?

Answer 1

There are 7 letters, but three 'o's are indistinguishable, so there are 7! ÷ 3! ways = 840 ways.

If the 'T' and the 't' are also considered to be indistinguishable (that is ignoring the case of the letters; making "Toronto" and "toronTo", etc the same), then the number of ways is 7! ÷ (3! x 2!) ways = 420 ways.

! after a number means the factorial of the number which is the product of all numbers less than or equal to the number, and greater than or equal to 1. Thus:

7! = 7 x 6 x 5 x 4 x 3 x 2 x 1.

3! = 3 x 2 x 1

2! = 2 x 1

0! is defined to be 1.