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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

### 1 comment

explanation:

_ _ _  I have three places to fill for numerals(0-9) their are 10 choices ,26 choice for small alphabet and 26 choice for capital alphabet,

10*26*26

but dont forget all are distinct so we have to multiple it with 3 factorial for different order

10*26*26*3*2=40560

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

### 1 comment

c is correct option

## 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

by
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.

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