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How many distinct passwords are possible?

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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

3 Answers

1 1 vote

Ans – (C) 40560

Choices of numbers = 10

Choices of uppercase letters = 26

Choices of lowercase letters = 26

There are three characters in a password, one from each category. 

If the positions were fixed, number of passwords possible = 10 * 26 * 26 = 6760

Accounting for changes in position, no of passwords possible = 3! * 6760 = 40560

1 1 vote
An E-Mail password must contain three characters eg(_ _ _).

→ One character will be one numeral from 0 to 9.

Number of choices =10C1=10

→ Second character will be upper case letter from the English alphabet.

Number of choices =26C1=26

→ Third character will be lower case letter from the English alphabet.

Number of choices =26C1=26

→ We can arrange these three characters in 3! ways i.e. 6 ways.

Total number of distinct passwords = 10 × 26 × 26 × 6 = 40,560.
0 0 votes
Answer is Option A – 6760

Loggic

0-9 → total 10 characters

a-z → total 26 characters

A-Z → total 26 characters

now password must be 3 character and must contain 1 numerical , 1 small alphabate and 1 capital alphabet.

10*26*26 = 6760
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