![]() ![]() For instance, the arrangements ASE (using the first “S”) and ASE (using the second “S”) will count as one only. In a distinguishable permutation, we count those arrangements as one if they contain the repeated element. Notice that one of its elements (the letter “S”) is repeated twice.ĭistinguishable permutations refer to the number of ways we can arrange the given objects if some elements of these objects are repeated in the set. What if some objects in a set are repeated? How are we going to find their permutations?įor example, suppose that we want to find the total number of ways to arrange the letters of the word ASSURE. Thus, five people can arrange themselves for picture-taking 120 times. Solution: In this problem, we have n = 5 (since there are five people given in this problem) and r = 5 (since we are taking all five people at a time). Sample Problem 2: How many ways can five people arrange themselves for picture-taking? Solution: In this problem, we have n = 4 (MATH has four letters) and r = 3 (since we are taking three letters at a time). ![]() Sample Problem 1: How many ways can you arrange the letters of the word MATH, taking three letters at a time? Let us solve more permutation problems below. Sixty three-digit numbers can be formed using the numbers 2, 4, 6, 8, and 9. Let the three blanks below represent a three-digit number: Therefore, we must apply some mathematical techniques so we don’t have to perform such tedious tasks. If we try to list all the three-digit numbers that can be formed using the given numbers, it will take us a lot of time to list them. In this section, we will find out how we can determine the number of permutations or arrangements that can be formed from the given objects.įor example, how many three-digit numbers can you form using the numbers 2, 4, 6, 8, and 9?Īgain, this is an example of permutation since the order of the arrangement of the objects matter (e.g., arrangement 246 is distinct from 426 and 642). Thus, it cannot be considered a permutation. So, the order is not important in this situation. If you form a group of 12 players, even if you change the arrangements of the players in the set, they are still referring to the same group. Although the persons in the picture are the same, the arrangement change makes the “pictures” different. This is an example of a permutation since every time the four persons change their positions in the picture taking, they take different pictures.This example is not a permutation but instead a combination. ![]() Hence, the arrangement of the objects in this situation does not matter. Even if we change the arrangement of these persons (e.g., Francis, Mac, and Alexa), we are still referring to the same group. Suppose we form a group consisting of Alexa, Francis, and Mac. Hence, these arrangements are counted as two different things. For instance, although 246 and 642 are essentially the same digits, these numbers are different or distinct.
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