form a key for your lock containing the numbers 2 2 5 8 How many different keys can you form?

If we assume that the order of the numbers in the key matters, then we can form **24** different keys using the numbers 2, 2, 5, and 8. To see why, we can use the following formula: ``` n! / (n1! * n2! * ... * nk!) ``` where `n` is the total number of items, `k` is the number of distinct items, and `ni` is the number of times the `i`-th item appears. In this case, we have `n = 4`, `k = 3`, `n1 = 2`, `n2 = 1`, and `n3 = 1`. Substituting these values into the formula, we get: ``` 4! / (2! * 1! * 1!) = 24 / 2 = 12 * 2 = 24 ``` Therefore, we can form **24** different keys using the numbers 2, 2, 5, and 8, assuming that the order of the numbers in the key matters. I hope this helps!