In how many ways can the letters of the word TOTALITY be arranged?

Analyze the question

We need the number of distinct arrangements of the letters in TOTALITY. Some letters repeat, so we must account for that.

Concept

For n letters where some letters repeat, the number of distinct arrangements is:

n! / (p! × q! × ...)

where p, q, ... are the counts of each repeated letter.

Solution

Letters in TOTALITY: T, O, T, A, L, I, T, Y

• Total letters: 8
• T appears 3 times
• O, A, L, I, Y each appear once

Number of arrangements = 8! / 3!

8! = 40320 3! = 6

40320 / 6 = 6720

Answer

The number of arrangements is 6720, which matches option A.

Tip

For "arrange the letters of a word" questions, first count the total letters, then divide by the factorial of each repeated letter's count. A quick shortcut here: 8!/3! = 8×7×6×5×4 = 6720. You only multiply down from 8 for as many terms as needed, which saves time in the exam.