The number of terms in a multinomial expansion of m terms raised to the nth power is equal to C(n+m-1,n).
In the present case,
n=5, m=3, so
In the same vein, you may be interested to know that the individual coefficients for the terms
a^p*b^q*c^r (where p+q+r=n)
For example, the term a²b²c
so the coefficient is
For more interesting facts, see: