Question

A password is 4 characters long, consisting of 2 letters and 2 numbers. The password must begin and end with a letter. If numbers can be repeated but letters cannot, how many possibilities are there?
a.
65,000
b.
60,840
c.
58,500
d.
52,650

Answer 1

We need letters in positions 1 and 4 (no repeats) and digits in positions 2 and 3 (repeats allowed).

Choices: 26 choices for the first letter, 10 choices for each digit, and 25 choices for the final letter.

Total = 26 × 10 × 10 × 25 = 65,000.

Answer: a. 65,000