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Real-Life Math

You work as a dolphin researcher in sunny Hawaii, where you have just completed an experiment with the dolphins. You wanted to discover the dolphins' understanding of an artificial sign language.

You evaluated the number of times the dolphins got the signed commands correct. The results were recorded. Now you need to analyze them to determine whether it was just luck that the dolphins got the commands right or whether the dolphins actually understood the signs. To do this, you need to calculate the total number of sign combinations that are possible.

For example, if there are two possible sign sequences and the dolphins get half of them right, then it is probably luck.

But if you have 2,000 sign sequences possible and the dolphins get most of them right, then you've really got something!

The dolphins that you've been working with know 25 commands. The length of each sign sequence is three commands.

How many possible sequences are there?

Hints:

The number of possible commands = n! / (r!(n - r)!)

n = total number of commands
r = number of commands in a sequence
! = factorial of the number

What's a factorial? Here's an explanation:

x! Or "x factorial" stands for x(x-1)(x-2)...1
5! = 5(4)(3)(2)(1)
5! = 120

You will need a scientific calculator to figure out the solution using the above method.

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