The chosen President has Calculus as a focus and the chosen Vice-President has Statistics as a focus?

Question

The Math Club is picking names out of a hat to determine who will serve as the Executive for their group. The person whose name is drawn first will serve as the President, and the person whose name is drawn second will be Vice-President. The Math Club has 13 members: 5 members whose focus of study is Statistics and 8 members whose focus of study is Calculus. [Hint: A tree diagram would be helpful in analyzing this problem.]

Answer 1

There are 8*5 = 40 ways to select someone with Calculus as a focus as President and Statistics as a focus as Vice-President. There are P(13,2) = 13*12 = 156 ways to select someone as President and another as Vice-President. Then, the probability of selecting someone with Calculus as a focus as President and Statistics as a focus as Vice-President is 40/156 = 10/39