Final answer:
15,120 different five-letter codes can be formed from the letters in EDUCATION.
Step-by-step explanation:
To find the number of different five-letter codes that can be formed from the letters in EDUCATION, we can use the concept of permutations. A permutation is an arrangement of objects in a specific order.
In this case, we have 9 letters to choose from (E, D, U, C, A, T, I, O, N) and we need to choose 5 of them. Since order matters (e.g., EDUCA and CAEDU are considered different codes), we can use the permutation formula:
nPr = n! / (n - r)!
where n is the total number of objects to choose from and r is the number of objects we need to choose.
Plugging in the values, we get:
9P5 = 9! / (9 - 5)! = 9! / 4! = (9 * 8 * 7 * 6 * 5!)/(4 * 3 * 2 * 1) = 15,120.
Therefore, there are 15,120 different five-letter codes that can be formed from the letters in EDUCATION.