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.