Question

You have 6 reindeer, Prancer, Rudy, Balthazar, Quentin, Jebediah, and Lancer, and you want to have 3 fly your sleigh. You always have your reindeer fly in a single-file line. How many different ways can you arrange your reindeer?

Answer 1

120 ways.

Explanation:

We have been given that you have 6 reindeer, Prancer, Rudy, Balthazar, Quentin, Jebediah, and Lancer, and you want to have 3 fly your sleigh. You always have your reindeer fly in a single-file line.

We will use permutation formula to solve our given problem as:

`_(r)^(n)\textrm{C}=(n!)/((n-r)!)`

`_(3)^(6)\textrm{C}=(6!)/((6-3)!)`

`_(3)^(6)\textrm{C}=(6\cdot 5\cdot 4\cdot 3!)/(3!)`

`_(3)^(6)\textrm{C}=6\cdot 5\cdot 4`

`_(3)^(6)\textrm{C}=120`

Therefore, you can arrange your reindeer in 120 different ways.