Find the total distinct 4 letter code arrangments

Question

how many distinct 4-letter code words can be made from the letters in the word ALGEBRA?

Hello, I am currently competing in what is known as UIL Mathematics, a competitive Math event. I have tried the theory of getting the total amount of letters followed by "!" and dividing by the repeating letters followed by "!" but this didn't give the answer. I did this: 7!/2!. Please help.

Answer 1

Hint:

How many ways can you choose a four letter code using letters from the word ALGEBR

The above codes will all have zero or one A.

Now, how many ways can you choose a four letter code where there are exactly two A's being used and the remaining two letters are taken from LGEBR.

Answer 2

Following @JMoravitz's hint, there should be

$P^6_4+P^5_2\cdot C^4_2=360+20\cdot6=480$.