You have 5 reindeer 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

60 different ways

Step-by-step explanation:

According to the given data, we have

Number of reindeer i.e 5

Number of them fly their sleigh i.e 3

In order to find  different ways can you arrange your reindeer, we will use "Permutation":

considering, n = 5 and r=3

it becomes,

5P3= 60 (by using calculator)

OR

5P3 = 5!/ (5-3)!

5P3=120 / 2

5P3= 60

Thus, ways can you arrange your reindeer in 60 different ways

the quotient is 4x^2 - 27x + 167 with a remainder of -996

step-by-step explanation:

in synthetic division, use -6 as the divisor and use the coefficients {4, -3, 5, 6}:

-6     )   4     -3     5     6

                -24   162 -1002

          4   -27   167   -996

thus, the quotient is 4x^2 - 27x + 167 with a remainder of -996.

note:   your "4x°-3x+5x+6" is ambiguous / incomplete.   i had to assume that you meant '4x^3 - 3x^2 + 5x + 6."