Final answer:
There are 120 unique four-digit numbers that can be formed from the digits 2, 3, 4, 5, and 6 without repetition, calculated by multiplying the number of possibilities for each digit position together (5 × 4 × 3 × 2).
Step-by-step explanation:
To determine how many four-digit numbers can be formed from the digits 2, 3, 4, 5, and 6 without repetition, we can use permutations. The first digit has 5 possibilities (2, 3, 4, 5, or 6), the second digit has 4 remaining possibilities after the first digit is chosen, the third digit has 3 possibilities, and the fourth digit has 2 possibilities. So, we multiply these together to find the total number of unique combinations.
The calculation is 5 × 4 × 3 × 2, which equals 120. Therefore, there are 120 different four-digit numbers that can be formed using the given digits without repetition.
This use of permutations is a basic concept in combinatorics, a branch of mathematics concerning the counting, arrangement, and combination of objects.