- #1

- 2,544

- 3

## Homework Statement

A software company uses a 20 character product key that new buyers of their

product must use during installation to successfully install the software in their

computers. The structure of these product keys is as follows. Repetitions are

allowed unless explicitly forbidden. Reading from left to right

(1) The first five characters must be capital letters from the western alphabet;

(2) The second five characters must include at least two of the digits 0, 1, 2, 3,

4, 5, 6, 7, 8, 9, and must include at least one capital letter;

(3) The third five characters are unrestricted - they may be digits or they may

be capital letters;

(4) The final five characters must include an 8.

## The Attempt at a Solution

1) [itex] 26^5 [/itex]

2) On this one I will take the total number of combinations and subtract the combinations that just have letters in them to leave me with the total number of combinations that have numbers in them, then i need to subtract the combinations that just have one number so i can make sure my combinations have at least 2 numbers

[itex] 36^5-26^5-26^4*10 [/itex]

3) [itex] 36^5 [/itex]

4) [itex] 36^4 [/itex]

because I have 1 choice for one slot and then 36 on the rest.