# Math Help - trinomials

1. ## trinomials

How many different terms are there in the expansion of (x+y+z)^20?

2. ## Re: trinomials

Answer is C(22,2). But I want to learn the logic of it.

3. ## Re: trinomials

Originally Posted by kastamonu
Answer is C(22,2). But I want to learn the logic of it.
If we select $N$ items from $K$ different choices (where repetition is allowed), the number of ways that can be done is $\dbinom{N+K-1}{N}$.

In expanding $( x+ y+ z)^{20}$ each term looks like $Ax^jy^kz^m$ where $j+k+m=20$.

So we are choosing $20$ ones from $3$ kinds: $\dbinom{22}{2}$.

many thanks