Factorial
Example 1: How many 3 digit numbers can you make using the digits 1, 2 and 3 without
repetitions?
method (1) listing all possible numbers using a tree diagram.
We can make 6 numbers using 3 digits and without repetitions of the digits.
method (2) counting:
LOOK AT THE TREE DIAGRAM ABOVE.
We have 3 choices for the first digit, 2 choices for the second digit and 1 choice for the third digit.
Using the counting principle, we can say:
The total number of 3digit numbers is given by
3 * 2 * 1 = 6
There is a special notation for the product 3 * 2 * 1 = 3! and it is read 3 factorial.
In general n! is read n factorial and is given by
n! = n*(n  1)*(n  2)*...*2*1
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We also define 0! = 1.
Example 2: How many different words can we make using the letters A, B, E and L ?
Solution: We have 4 choices for the first letter, 3 choices for the second letter, 2 choices for the
third letter and 1 choice for the fourth letter. Hence the number of words is given by
4 * 3 * 2 * 1 = 4! = 24
Permutations
Example 3: How many 2 digit numbers can you make using the digits 1, 2, 3 and 4 without
repeating the digits?
This time we want to use 2 digits at the time to make 2 digit numbers.
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 Fall '10
 DrSajid
 Numerical digit, 2 digits, 2 digit

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