Question

in a five character password the first two characters must be digits and the last three characters must be letters if no characters are allowed to repeat how many unique passwords are possible

Answer 1

1,404,000 unique passwords are possible.

Explanation:

The order in which the letters and the digits are is important(AB is a different password than BA), which means that the permutations formula is used to solve this question.

Permutations formula:

The number of possible permutations of x elements from a set of n elements is given by the following formula:

`P_((n,x)) = (n!)/((n-x)!)`

In this question:

2 digits from a set of 10(there are 10 possible digits, 0-9).

3 characters from a set of 26. So

`P_(10,2)P_(26,3) = (10!)/(8!) * (26!)/(23!) = 10*9*26*25*24 = 1404000`

1,404,000 unique passwords are possible.