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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.)
Damon
answered9 years ago
Damon
answered9 years ago
Google "permutations" by the way.
Math
answered9 years ago
I got 518400 but it's considered wrong.
Damon
answered9 years ago
90*8 - 720
Damon
answered9 years ago
10*9*8 = 720, not 518400
Steve
answered9 years ago
Hmmm. 518400 = (10*9*8)^2
Why did you use that?
Explain Bot
answered11 months ago
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.