Question

You have 666 reindeer, Prancer, Rudy, Balthazar, Quentin, Jebediah, and Lancer, and you want to have 333 fly your sleigh. You always have your reindeer fly in a single-file line.
How many different ways can you arrange your reindeer?

How many unique ways are there to arrange the letters in the word DEN?

Answer 1

Answer:

a) 120 ways

b) 6 unique ways

Step-by-step explanation:

The question will be solved using the permutation formula since are arranging. Permutation deals with arrangement.

If there we are to arrange n objects taking 'r' at a time, this can be done in nPr ways.

$nPr = \frac{n!}{(n-r)!}$

a) If you therefore have 6 reindeer, Prancer, Rudy, Balthazar, Quentin, Jebediah, and Lancer, and you want to have 3 fly your sleigh. Since they are in a single file line, This can be done in 6P3 number of ways.

$6P3 = \frac{6!}{(6-3)!}\\ 6P3 = \frac{6!}{3!}\\ 6P3 = \frac{6*5*4*3!}{3!} \\6P3 = 6*5*4\\6P3 = 120\ ways$

b) The number of unique ways to arrange the letters in the word DEN is 3! ways since there are only 3 letters in the word.

3! = 3*2*1

3! = 6ways