In general permutating r (2 digit in the above example) items out of a set of n (4 digits in the above example) items is written as n P r and the formula is given byĦ P 5 = 6! / (6 - 5)! = 6×5×4×3×2×1 / 1! = 720Ĥ P 4 = 4! / (4 - 4)! = 4! / 0! = 4! = 4×3×2×1 = 24 (We now understand the need to define 0! = 1)Įxample 5: How many 3 letter words can we make with the letters in the word LOVE? When you use the digits 3 and 4 to make a number, the number 34 and 43 are different hence the order of the digits 3 and 4 is important. The most important idea in permutations is that order is important. The above problem is that of arranging 2 digits out of 4 in a specific order. Using the counting principle, the number of 2 digit numbers that we can make using 4 digits is given by This time we want to use 2 digits at the time to make 2 digit numbers.įor the first digit we have 4 choices and for the second digit we have 3 choices (4 - 1 used already). Hence the number of words is given byĮxample 3: How many 2 digit numbers can you make using the digits 1, 2, 3 and 4 without repeating the digits? 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. In general n! is read n factorial and is given byĮxample 2: How many different words can we make using the letters A, B, E and L ? There is a special notation for the product 3 × 2 × 1 = 3! and it is read 3 factorial. The total number of 3-digit numbers is given by Using the counting principle, we can say:
We have 3 choices for the first digit, 2 choices for the second digit and 1 choice for the third digit. We can make 6 numbers using 3 digits and without repetitions of the digits. Method (1) listing all possible numbers using a tree diagram. Example 1: How many 3 digit numbers can you make using the digits 1, 2 and 3 without repetitions?
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