# RUN bank requires all internet banking customers to have a 4 digit password consisting of 2 lower case letters (a-z) followed by 2 number (0-9). Letters and numbers can be repeated. CAN Bank...

RUN bank requires all internet banking customers to have a 4 digit password consisting of 2 lower case letters (a-z) followed by 2 number (0-9). Letters and numbers can be repeated.

CAN Bank requires all internet banking customers to have a 4 digit password consisting of 3 upper or lowercase letters(a-z or A-Z) followed by one number (0-9). Letter can be repeated

1/ Calculate the possible number of passwords that can be generated for each bank.

2/ RUN Bank is considering to allow customers the use 2 upper or lower case letters followed by 2 numbers. What effect will allowing customers to use upper case letter have on the number of different passwords that can be generated?

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### 1 Answer

Possible number of passwords for **RUN bank**:

4-digit consisting of 2 lower case letters (a-z, 26 options for each) followed by 2 numbers (0-9, 10 options each)

No. of combinations = 26 x 26 x 10 x 10 = **67600**

Possible number of passwords for **CAN Bank**:

4-digit consisting of 3 upper or lower case letters (a-z or A-Z letters, 52 options each) followed by one number (0-9, 10 options)

No. of combinations = 52 x 52 x 52 x 10 = **1406080**

If RUN bank customers are allowed the use of upper or lower case letters instead of only lower case ones, no of possible combinations will increase.

No. of possible combinations (with lower or upper case letters)

= 52 x 52 x 10 x 10 = **270400**

In other words, number of password combinations will be four-times as many as compared to original scenario.

Hope this helps.