An e-mail password must contain three characters. The password has to contain one numeral from 0 to 9, one upper case and one lower case character from the English alphabet. How many distinct passwords are possible? A. 6,760 B. 13,520 C. 40,560 D. 1,05,456

GATE 2018 · General Aptitude · Counting · medium

Answer: 40,560 distinct passwords are possible. Answer: C.

1. Count choices for each character type: Digit: 10 choices. Uppercase: 26 choices. Lowercase: 26 choices. Selection count = 10 * 26 * 26 = 6,760.
2. Multiply by the number of arrangements: Since the 3 characters are of distinct types, there are 3! = 6 ways to arrange them in the password. Total passwords = 6,760 * 6 = 40,560.