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?
6,760
13,520
40,560
1,05,456
ANSWER
The number of distinct passwords is , so the answer is option (C).
Official answer: CSource: Official answer key, GATE 2018 EE (IIT Guwahati)
Count the choices for each type of character. The numerals 0 to 9 give choices. The English alphabet has 26 letters, so there are upper case choices and lower case choices.
By the multiplication principle, the set of three characters (one of each type) can be chosen in ways.
A password is an ordered string, so the same three characters can be arranged in different orders. The three characters are of different types, so every arrangement gives a different password. Three distinct characters can be arranged in ways.
Total number of passwords:
This is option (C).
KEY IDEA
First choose which character of each type to use (). Then count the positions: the numeral, the upper case letter and the lower case letter can sit in any order, which gives arrangements. Every arrangement is a different password because the three characters are of different types.
WATCH OUT FOR
Stopping at (option A), which silently fixes the order as numeral, then upper case, then lower case. Some students multiply by 2 instead of and get 13,520 (option B). Others count every 3-character string over all 62 symbols, which gives and ignores the rule that the password needs one character of each type.
From the GATE 2018 EE paper. Every question of this paper · Download the full paper · All 58 Numerical questions, with notes
