Step-by-step Solution:

You are considering the number of one-to-one (injective) functions from a set \( \{1, 2, 3\} \) to a set \( \{a, b, c, d, e\} \). \[\] For a one-to-one function, each element in the domain must map to a distinct element in the codomain. Here's how we can calculate the number of one-to-one functions: \[\] The first element in the domain (1) can be mapped to any of the 5 elements in the codomain. \[\] The second element in the domain (2) can then be mapped to any of the remaining 4 elements in the codomain (since it must be distinct from the first mapping). \[\] The third element in the domain (3) can be mapped to any of the remaining 3 elements in the codomain. \[\] Thus, the total number of one-to-one functions is: \[ 5 \times 4 \times 3 = 60. \] So, the total number of one-to-one functions is 60.