One company's ID cards consist of 5 letters followed by 2 digits. How many cards can be made if repetitions are allowed? If repetitions are not allowed?

We are told that an ID card contains 5 letters and 2 digits. It is known that there are 26 letters and a total of 10 digits.

When repetitions are allowed, the total numbers of cards which can be made are computed as:

x=(26)²×(10)²

Solving the above equation, we have:

x=(26)²×(10)²

  =1188137600

Thus, the total numbers of cards that can be made when repetitions are allowed are 1,188,137,600.

When repetitions are not allowed, the total numbers of cards that can be obtained are estimated as:

y=(26×25×24×23×22)×(10×9)

Solving the above equation, we have:

y=(26×25×24×23×22)×(10×9)

   =710424000

Thus, the total numbers of cards obtained when repetitions are not allowed are 710,424,000.