Ministry of Education are inviting tender for four categories promoting the use of IT in education. Each category consists of 5, 4, 3, and 7 projects, respectively. Each project appears on exactly one category. How many possible projects are there to choose from? Explain your answer.

My Answer: $(5+4)+(4+4)+(3+3)+(7+4)=9+8+6+11=34$ possible projects to choose from. I used the sum rule here.

Is this correct?

My Answer: $(5+4)+(4+4)+(3+3)+(7+4)=9+8+6+11=34$ possible projects to choose from. I used the sum rule here.

Is this correct?