Answer:
Explanation:
The number of ways to arrange the letters in "HEDGEHOG" is 8!/(2!3!). The exclamation mark (!) means factorial, which is the product of all positive integers up to that number. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.
In this case, we have two H's and three E's, so we have to divide the total number of arrangements by the number of arrangements of H's and the number of arrangements of E's to avoid overcounting.
The total number of arrangements of the eight letters is 8!:
8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40320
The number of arrangements of H's is 2!:
2! = 2 x 1 = 2
The number of arrangements of E's is 3!:
3! = 3 x 2 x 1 = 6
So the number of arrangements of the letters in "HEDGEHOG" that avoid overcounting is:
40320 / (2 x 6) = 40320 / 12 = 3360.
Therefore, there are 3360 ways to arrange the letters in "HEDGEHOG".