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# probability - Factorial Example 1 How many 3 digit numbers...

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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 3-digit 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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probability - Factorial Example 1 How many 3 digit numbers...

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