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Permutation questions are about taking a group of objects and totaling how many ways we can arrange them in specific ways. Here is an example that we will explain later.
In how many ways can a pet shop line up 3 cats and 3 dogs in 6 cages if
the cats must be in the second, fourth, and sixth cages?
I. The Basics: Three Steps to Permutation Clarity
1. Figure out how many places there are to fill.
2. Figure out how many objects potentially can go into each place.
3. Multiply for the answer.
Example
How many outcomes are there when two identical dice are rolled?
Following the steps:
1. Figure out how many places there are to fill
Because there are two dice, there are two places to fill:
__ __
2. Figure out how many objects potentially can go into each place
Because each die has 6 different potential outcomes, we will fill the
spaces accordingly:
_6_ _6_
3. Multiply for the answer
_6_ × _6_ = 36
Example 2
In Country X, three digit area codes are to be given to each town. The first
digit will be any number from 2-9, inclusive, the second digit can only be either
0 or 1, and the third digit can be any number from 0-9, inclusive. How many
different area codes can be issued in Country X?
Following the steps:
1. Figure out how many places there are to fill
Because there are three digits, there are three places to fill: __ __ __
2. Figure out how many objects potentially can go into each place
The question states that the first digit can be any number from 2-9, inclusive.
There are therefore 8 potential options. The second digit can be only 0 or
1, therefore, there are 2 potential options. The third digit can be any number
from 0-9, inclusive, and there are 10 such numbers. The diagram looks like
this:
_8_ _2_ _10_.
3. Multiply for the answer
_8_ × _2_ × _10_ = 160
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