Question

Signals

The king has 10 (different) colored flags that he uses to send coded messages to his general in the field. For example, red-blue-green might mean “attack at dawn” and blue-green-red may mean “retreat.” He sends the message by arranging three of the flags atop the castle wall.

The maximum number of such coded messages is _______.

(Give your answer as a whole number.)

Answer 1

10! /(10-3)! = 10!/7! = 10*9*8

Answer 2

Google "permutations" by the way.

Answer 3

I got 518400 but it's considered wrong.

Answer 4

90*8 - 720

Answer 5

10*9*8 = 720, not 518400

Answer 6

Hmmm. 518400 = (10*9*8)^2

Why did you use that?

Answer 7

[AI-generated answer — Explain Bot]

To find the maximum number of coded messages that can be sent using the 10 different colored flags, we need to use the concept of combinations.

In this case, we are arranging 3 out of 10 flags, and the order in which they are arranged matters. We can use the formula for combinations to calculate the number of possibilities:

nCr = n! / [r! * (n - r)!]

Where n is the total number of items, r is the number of items we are selecting, and ! denotes the factorial function.

Substituting the values into the formula, we get:

10C3 = 10! / [3! * (10 - 3)!]

Now let's calculate this:

10! = 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 3,628,800
3! = 3 * 2 * 1 = 6
(10 - 3)! = 7!

Now we can substitute these values into the formula:

10C3 = 3,628,800 / (6 * 7!)
10C3 = 3,628,800 / (6 * 7 * 6 * 5 * 4 * 3 * 2 * 1)

After simplifying:

10C3 = 10 * 9 * 8 / (3 * 2 * 1) = 120

Therefore, the maximum number of coded messages that can be sent using the 10 different colored flags is 120.