You have 8 flags but you can only use 3 at a time. In this case, order does matter.

When order does matter, the arrangement is called a “permutation.” Permutations can be written as nPr, or in this case, 8P3.

n = the total number in the set

r = the number used in each permutation

To solve any permutation, use this formula:

n! / (n – r)!

The ! stands for “factorial.” You literally just multiply a number by itself and all the positive counting numbers that come before it. For example, 4! = 4*3*2*1 = 24

Okay, now you can solve the problem:

8P3 =

8! / (8 – 3)! =

8! / 5! =

(8*7*6*5*4*3*2*1) / (5*4*3*2*1)

Now to make things easier, cross off the like terms on each side of the division sign. The like terms should be: 5,4,3,2,1.

This will also eliminate the denominator.

= 8*7*6

= 336

ANSWER – there are 336 ways to arrange the flags.

There are 7 different choices for the second flag, because it can be any of the 8 flags except the top one that you have already chosen.

Similarly, there are 6 choices for the bottom flag.

These choices are all independent, so total possibilities = 8(7)(6) = 336, answer C).