The correct number of one-to-one functions from set A to set B is: 332,640.
To determine the number of one-to-one functions from a set with five elements (set A) to a set with 12 elements (set B), consider that one-to-one functions establish a unique pairing between each element in set A and an element in set B.
Initially, there are 12 options for where to send the first element of set A. Once the first element is mapped, there are 11 remaining options for the second element, and so on.
Therefore, the total number of one-to-one functions can be calculated as follows:
12 × 11 × 10 × 9 × 8 = 39,916,800
However, this calculation overcounts the actual number of one-to-one functions since it doesn't consider the order in which the elements are mapped. For instance, mapping element 1 to element 12 in set B and element 2 to element 11 is considered a different function than mapping element 2 to element 12 and element 1 to element 11.
To account for this overcounting, we need to divide the initial calculation by the number of permutations of five elements, which is 5! = 5 × 4 × 3 × 2 × 1 = 120.
Therefore, the correct number of one-to-one functions from set A to set B is:
39,916,800 ÷ 120 = 332,640