How many distinct rearrangements are there of the letters in the word DISTINCT?

1. The word has 8 letters, so if all were distinct there would be 8! orderings. 2. 8! = 40,320. 3. The letter I appears twice and the letter T appears twice, so many of those orderings are duplicates. 4. Divide by 2! for the two I letters and by 2! for the two T letters. 5. That gives 40,320/(2 times 2) = 40,320/4. 6. So there are 10,080 distinct arrangements. 7. Dividing by only one 2! gives 20,160, which corrects for one repeated letter but forgets the other. _Source: OpenStax Algebra and Trigonometry (CC BY 4.0), Ch 13 "Sequences, Probability and Counting Theory", section 13.5 Counting Principles_