ACT Maths question help?

Test Preparation
1

How would you go about solving this problem? I am completely lost :frowning:
please write out all your steps and workings!

When she chooses a password, Eloise always uses exactly 10 different characters: five letters (A, B, C, D and E) and five numbers (2, 3, 4, 5 and 6). Additionally, she always ensures that no pair of letters is consecutive and that no pair of numbers is consecutive. how many different passwords conform to these rules?

(F) fewer than 1000
(G) between 1,000 and 10,000
(H) between 10,000 and 100,000
(J) between 100,000 and 1,000,000
(K) more than 1,000,000

thank you! I’d really appreciate some help!!

2

H

3

how did you get that answer?

4

@stardust4321 given the conditions, the 10-letter password must alternate letter and number. We have two cases, depending on if it starts with a letter or a number.

If the password begins with a letter, we have (5!)(5!) = 14400 possible passwords (why?).

If the password begins with a number, we also have 14400 possible passwords.

Therefore there are 14400 + 14400 = 28800 possible passwords total, H.

5

thank you!