Question

There are 18 pieces of music to choose from: 6 for piano, 5 for violin, and 7 for guitar. In

how many ways can you choose 3 pieces of music, if at least 1 must be for piano?

Explain your reasoning. (3 marks)

Answer 1

$$\dbinom{6}{1}\dbinom{5+7}{3-1}+\dbinom{6}{2}\dbinom{5+7}{3-2}+\dbinom{6}{3}\dbinom{5+7}{3-3}$$

$$=6(66)+15(12)+20(1)=596$$