How many six-character code words can be formed if the first two characters are letters and the others are letters and/or digits?

Question

How many six-character code words can be formed if the first two characters are letters and the others are letters and/or digits?

IF REPETITION ISNT ALLOWED

Answer choices;

A)918,918,000

B)723,465,600

C)1,135,420,416

D)918,918,000

Answer 1

One way to think about a problem like this one, is to think about how many choices you have for each character. Multiplying the number of choices for each character together, will give you to total number of possibilities.

Remember that repetition is not allowed.

So, we have 26 choices for our first letter character, and 25 choices for our second letter character, since we can't choose the same letter as we did for the first one.

Similarly, we have 24+10=34 choices for our third character(24 remaining letters and 10 digits), 33 choices for our fourth character, 32 for the fifth, and 31 for the sixth.

Therefore, the total number of possibilities is 26x25x34x33x32x31 = 723,465,600