Answer to Question #217833 in Algebra for joe

Question

how many different computer passwords are possible if 

(a) digits and letters can be repeated

(b) digits and letters cannot be repeated

Question:  3 digits followed by 2 letters

Answer 1

We need to generate computer password of 3 digits followed by 2 letters

Total number of digits is 10

Total number of letters is 26

Then

a) Digits and letters can be repeated

For the first digit,we have 10 options

For the second digit,we have 10 options

For the third digit,we have 10 options

For the first letter, we have 26 options

For the second letter, we have 26 options

The total combination will be equal to the

$10×10×10×26×26\\=676000$

So the total possible different computer password in this case is 676000

b) Digits and letters cannot be repeated

In this case

For the first digit,we have 10 options

For the second digit,we have 9 options

For the third digit,we have 8 options

For the first letter, we have 26 options

For the second letter ,we have 25 options

Total possible password in this case will be

$10×9×8×26×25\\=468000$

So the total possible different computer password in this case is 468000