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$?$

1. $6,760$
2. $13,520$
3. $40,560$
4. $1,05,456$

## 1 Answer

Here password is consist of 3 characters;

_ _ _

1. First dash can be fill with 0 to 9 numbers: so total possibilities are 10.
2.  Second dash can be fill with 26 letters which are UPPERCASE : Total possibilities are 26
3. Third dash can be fill with 26 small letters: total possibilities are 26

thus total no of distinct password are : 26*26*10 = 6760

but take an eg, a A 0 it can be arrange in 6 different ways

1. a 0 A
2. a A 0
3. 0 a A
4. 0 A a
5. A a 0
6. A 0 a

thus total possible arrangement can be 6760*6 = 40560 (distinct possible ways for a password).

480 points
Answer: