Real-Life Math -- Solution
Don't be intimidated by those factorials! While the numbers
are huge, they can be easily handled using a scientific calculator. Make sure
you know how to use the factorial and memory functions on your calculator
before you start. Here goes:
The number of possible commands
is= n! / (r!(n - r)!)
n = 25 (total number of commands)
r
= 3 (number of commands in a sequence)
! = factorial of the number
x
= n! / (r!(n - r)!)
Plug the values into the equation:
x
= 25! / (3! (25 - 3)!)
Solve the subtraction:
x = 25!
/ (3! (22)!)
Using your calculator, determine the value of the
denominator. Load it into your calculator's memory:
x = 25!
/ (6 x 1.124000727778e+21)
x = 25! / 6.744004366666e+21
Now,
solve the equation:
x = 1.551121004333e+25/ 6.744004366666e+21
x
= 2,300
The number of possible combinations is: 2,300
This
is real-life math based on the work of Mark Holder, a behavioral
neuroscientist.
In his research, there were over 2,000 possible sequences.
The dolphins responded correctly to 92 percent of the signs they were given.
That proved that the dolphins understood most of what they saw signed.
Surprisingly,
Holder found the dolphins responded better to people who were unfamiliar with
the commands -- the dolphins responded correctly to these commands 96 percent
of the time.
Holder hypothesizes that the reason the dolphins did better
with strangers is because they had to "listen more closely" and "pay more
attention" than they did to him. In human terms, it's like getting directions
from someone with a thick accent -- you have to listen more closely.