![]() Total number of elements in the word = n = 8 In how many ways the alphabets of the word ELECTRIC can be arranged? Solution Hence, shoes can be arranged on the shoe rack in 90 ways. This is an example of permutation with repetition because the elements are repeated and their order is important. The total number of pair of shoes = n = 6 How many different arrangements of shoes are possible? Solution He wants to put all these pairs of shoes on the shoe rack. Put the above values in the formula below to get the number of permutations:Įxample 3 John owns six-colored pair of shoes (two red, two blue and two black). This is an example of permutation with repetition because the elements of the set are repeated and their order is important. How many different flag combinations can be raised at a time? Solution ![]() Hence, the letters in the word EXCELLENT can be arranged in 30240 ways.Įxample 2 A ship must raise eight flags at one time (two red, two blue, and four green). Substitute these values in the formula below to get the number of ways in which the letters of this word can be arranged: Total number of elements in the word = n = 9 In how many ways can the alphabets of the word EXCELLENT be arranged? Solution We will substitute the above values in the formula below: In this example, the order of elements matter, and digits are repeated. How many eight-digit numbers can be formed with the numbers 2, 2, 2, 3, 3, 3, 4, 4? Let us solve the following example through the above formula to make the whole concept clearer. The formula that should be used while computing the permutations in such cases is given below: Since the items are repeated, therefore such scenarios are also examples of permutations with repetition. There is a separate formula to compute permutations in such problems. The question arises what shall we do in this case? Well, the answer is simple. Sometimes we are given a problem in which the identical items of type 1 are repeated "p" number of times, type 2 are repeated "q" number of times, type 3 are repeated "r" number of times, and so on. Hence, 10000 permutations are possible if we want to make a four-digit number from the set of the first 10 natural numbers. Therefore, we will get permutations by substituting the values in the following formula: The total number of elements in a set is 10 and the number of digits we want to select from this set is 4. Therefore, it means that it is an example of permutations with repetition. In all these numbers, one digit is repeated twice or thrice. Here, first, we need to determine whether we can choose a digit twice or not. How many different permutations are possible? K = number of elements selected from the setįrom the set of first 10 natural numbers, you are asked to make a four-digit number. The formula for computing the permutations with repetitions is given below: Permutations with repetition mean we can select one item twice. We know that in the permutations, the order of elements is important. In this article, we will specifically discuss permutation with repetition. It means that the selection of code from the first five whole numbers is an example of the permutation. If the order of the digits is changed, then the pin code will not work. Of course not, the order of the digits is important. Can he rearrange the digits as 3014 or 0143 etc.? Harry wants to make a pin code by choosing 4 digits from the set of first five whole numbers (0,1,2,3,4). You have already read an example of a simple combination above when three things are put in a bowl. In other words, we can say that the permutation is an ordered combination. ![]() The primary difference between the combination and permutation is that the order matters in permutation while it does not matter in combination. We always study combination with permutation in mathematics because there are many similarities between these two terms. The order of elements is not important in a combination. In mathematics, the combination means the number of ways in which different objects are combined to form a set. We are not concerned with the order in which these three things were put in the bowl. For instance, if anyone says that my bowl has a combination of apples, carrots, and bananas, then we immediately think that the bowl has three items. When we hear the word "combination" in our daily life, we immediately think about the collection of things in the form of a set or a group.
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