what is the total number of distinct terms in the expression (a+b+c)^15 ?

Question

Binominal problem

Answer 1

Treat this as (a+(b+c))^15 this produces an expression with 16 terms: a^15+a^14(b+c)+a^13(b+c)^2+...+a(b+c)^14+(b+c)^15; but the second term expands to 2 terms; the third term expands to 3; the fourth to 4 and so on. So we have 1+2+3+...15+16 terms. This sums to 16*17/2=136 terms.