Question

A school's choir is holding rehearsals for the lead singers in a show. There are 2 spots available with 6 people trying out. How many different singing combinations are there?

The answer provided is 15, but I don't know how they got to that number

Answer 1

15

Explanation:

This is because there is a total of 5 combinations for the first person to be paired with. People often make the mistake of counting the 5 among all of the candidates but as you go up in the participants, there is less combinations to be had. So the second would only have four possible pairings, third would have 3, fourth 2 and fifth 1. When you add them all up you would get 15 to be your grand total.