There are three different types of animal posters for sale. In how many different ways can I buy 8 animal posters if I want at least

Unsure if my solution is right. Might need a mod to confirm.

 

So you have 3 posters and you need at least 1 of each.

 

Let x, y, and z be the 3 different posters.

 

Since you need at least 1 of each poster, you have 7 ways to pick x, 6 ways to pick y, and 5 ways to pick z.

 

Use the Binomial Theorem and you get \(\frac{7!}{3!(7-3)!}+\frac{6!}{3!(6-3)}+\frac{5!}{3!(5-3)!}=65\).

 

I'm not sure if I did this problem right ;-;