Question

A ballroom dance couple has learned 13 different routines and needs to pick 10 of them to prepare for an upcoming local competition. How many different ways could they choose which dances to prepare?

Answer 1

We conclude that exist 286 different ways.

Explanation:

We know that a ballroom dance couple has learned 13 different routines and needs to pick 10 of them to prepare for an upcoming local competition.

So, we count that out of 13 different routines we choose 10.

We use the following formula:

`C_(10)^(13)=(13!)/(10!(13-10)!)=(13\cdot 12\cdot 11\cdot 10!)/(10!\cdot 3\cdot 2\cdot 1)=286\\`

We conclude that exist 286 different ways.