You have 6 reindeer, rudy, jebediah, ezekiel, lancer, gloopin, and balthazar, and you want to have 5 fly your sleigh. you always have your reindeer fly in a single-file line.
how many different ways can you arrange your reindeer?

Step-by-step

6 reindeer, from which we fly 5, in N1 ways.

Each of the five must be arranged in N2 ways.

The total number of arrangements is therefore N1*N2 arranglements.

Note: C(n,r) = n!/((r!(n-r)!)

N1 = 6 choose 5 = C(6,5) = 6!/(5!/1!) =  6 ways

(same as number of ways to choose 1 reindeer to be left out).

N2 = 5! ways (5 choices for the first, 4 choices for the second, 3 for the third, and 2 for the fourth, and 1 for the last) = 5*4*3*2*1 = 120 ways.

So total number of arrangements

= N1 * N2 = 6 * 120 = 720 ways.

Alternatively, you can line up the 5 vacant spaces and choose the first among 6 reindeer, second among 5, third among 4, fourth among 3, and the last one among 2 for a total of

6*5*4*3*2 = 720 arrangements.

explanation:

step-by-step explanation: