![]() ![]() We can show this mathematically using the permutations formula with n = 3 and r = 2 ![]() Our options are: RG, GR, RP, PR, GP and PG. How many unique permutations will we have if we cannot repeat balls?Ħ different ways. Let's say that we wanted to pick 2 balls out of a bag of 3 balls colored red (R), green (G) and purple (P) 1 2 3 Examples of permutations Permutations without repetitions ![]() Permutations Calculator What is a permutation?Ī permutation is a selection of r items from a set of n items where the order we pick our items matters. We can see examples of this type of combinations when buying ice cream at an ice cream store since we can select flavors more than once (I could get two, three or even four scoops of chocolate ice cream if I wished) and I don't care about which scoop goes on top (so chocolate on top and vanilla on the bottom is the same to me as vanilla on top with a chocolate base). We can count the number of combinations with repetitions mathematically by using the combinations with repetitions formula where n = 3 and r = 2. Our options are: RR, RG, RP, GG, GP and PP. If each time we select a ball we place it back in the bag, how many unique combinations will we have?Ħ different ways. Let's say that we wanted to pick 2 balls out of a bag of 3 balls, colored red (R), green (G) and purple (P) 1 2 3 We cannot select a team member more than once (so we can't have a team with Danny, Danny and myself) and we do not care about who is selected first to the team (so if I am in a team with Bob and Tom it is the same to me as being in a team with Tom and Bob). We can see examples of this type of combinations when selecting teams for a sports game or for an assignment. We can count the number of combinations without repetition using the nCr formula, where n is 3 and r is 2. How many unique combinations will we have if we cannot repeat balls?ģ different ways. Let's say that we wanted to pick 2 balls out of a bag of 3 balls colored red (R), green (G) and purple (P). Examples of Combinations Combinations without repetitions I will go through two more examples, but I will ignore every instance of #1!# since #1! =1#.Combinations Calculator What is a Combination?Ī combination is a selection of r items from a set of n items such that we don't care about the order of selection. So the amount of permutations of the word "peace" is: For example, in the word "peace", #m_A = m_C = m_P = 1# and #m_E = 2#. Each #m# equals the amount of times the letter appears in the word. Where #n# is the amount of letters in the word, and #m_A,m_B.,m_Z# are the occurrences of repeated letters in the word. ![]() The second part of this answer deals with words that have repeated letters. There are computer algorithms and programs to help you with this, and this is probably the best solution. As you can tell, 720 different "words" will take a long time to write out. To write out all the permutations is usually either very difficult, or a very long task. To calculate the amount of permutations of a word, this is as simple as evaluating #n!#, where n is the amount of letters. For the first part of this answer, I will assume that the word has no duplicate letters. ![]()
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