Question

How many terms are there in the expansion (x + y + z)^10?

Answer 1

for trinomial expansion the num of terms creates the following sequence:

3,6,10,15,21,28,36,45,55,66,78 ...

the 10th in the sequence is 66
there are 66 terms in (x+y+z)^10

Answer 2

alternative :
The number of terms of an expanded trinomial is

1/2 (n+1)(n+2)

in this case, n = 10
1/2 (10+1)(10+2) = 66