How many permutations of {A, B, C, D, E, F, G, H, I} are there in which the first character is A, B, or C and the last character is G, H, or I?

Question

I understand that it would be n! permutations for the given amount of elements, but I am not sure calculate it with these parameters.

Answer 1

3 for the first

3 for the last

(n-2)! for the rest.

Multiply them together.

Answer 2

Choose the first character.

Choose the last character.

How many ways can you order the remaining $7$?

$3 x 3 x 7!$

Answer 3

3 options for last place simultaneously 3 for first place, now we have 7 objects left. so 7 objects, 7 places which is 7! so answer is 3 3 7!