Finite math question

Question

A software development group uses randomly generated computer file names for security. If each name must be created by selecting two letters, with repeats allowed, from the set {a, b, c, d} followed by three digits, repeats not allowed, from the set of numbers{1, 2, 3, 4, 5, 6, 7}, how many filenames can be created?

Answer 1

To find the total combinations, first individually find the possible combinations of letter and numbers, then multiply those values together.

Letters: There are 4 letters, and since repeats are allowed, N_Letters = 4² = 16.

Numbers: There are 7 possible digits, and since repeats aren't allowed, N_Nums = 7•(7-1)•(7-2) = 210.

Thus the total combinations is 16•210 = 3,360 possible filenames.