Answer:
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.
[tex]nPr = \frac{n!}{(n-r)!}[/tex]
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.
[tex]6P3 = \frac{6!}{(6-3)!}\\ 6P3 = \frac{6!}{3!}\\ 6P3 = \frac{6*5*4*3!}{3!} \\6P3 = 6*5*4\\6P3 = 120\ ways[/tex]
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