So I think it never hurts to do as many examples. I've been struggling for over a week with this.Įxposed to permutations and combinations it takes a little bit to get your brain around it, Leaving us with the FIRST PERMUTATION that was counted or ONE COMBINATION of those 4 letters. Essentially, what the k! is doing by dividing the TOTAL PERMUTATIONS, is it is canceling all the additional permutations that were counted MORE THAN ONCE in the permutations formula. But were not counting permutations only COMBINATIONS, thus all we want to count is the FIRST PERMUTATION of the four letters. That means ABCD is 1 COMBINATION but it has 4! PERMUTATIONS (ABCD, ADCB, DCBA.etc). In light of this, it becomes clear that the permutation formula is counting one combination k! times, k = the number of chairs or spots (4 in the video). This reminded me of the principle of Inclusion/Exclusion which is basically about subtracting over counted elements. It's deceiving because the k! is actually DIVIDING the entire permutation equation. The part that confused me about the combinations formula is what the multiplication of k! in the denominator is doing to the formula. the number of permutations is equal to n!/(n-k)! so the number of combinations is equal to (n!/(n-k)!)/k! which is the same thing as n!/(k!*(n-k)!). So the formula for calculating the number of combinations is the number of permutations/k!. The group size can be calculated by permuting over the number of chairs which is equal to the factorial of the number of chairs(k!). So the number of combinations is equal to the number of permutations divided by the size of the groups(which in this case is 6). If we didn't care about these specific orders and only cared that they were on the chairs then we could group these people as one combination. So some of the permutations would be ABC, ACB, BAC, BCA, CAB and CBA. In our example, let the 5 people be A, B, C, D, and E. The number of combinations is the number of ways to arrange the people on the chairs when the order does not matter. So the formula for the number of permutations is n!/((n-k)!. For n people sitting on k chairs, the number of possibilities is equal to n*(n-1)*(n-2)*.1 divided by the number of extra ways if we had enough people per chair. We can make a general formula based on this logic. So the total number of permutations of people that can sit on the chair is 5*(5-1)*(5-2)=5*4*3=60. On the third chair (5-2) people can sit on the chair. On the second chair (5-1) people can sit on the chair. If there are 3 chairs and 5 people, how many permutations are there? Well, for the first chair, 5 people can sit on it. The formula for permutation is n! / (n-r)!, while the formula for combination is n! / r!(n-r)!.Ok, let's start by an example.The permutation is denoted as nPr or P(n,r), while the combination is denoted as nCr or C(n,r).A permutation is used when the arrangement or order of elements is important, while a combination is used when only the selection of elements matters.Permutation considers the order of elements, while combination does not.NCr = n! / r!(n-r)! where n is the total number of objects and r is the number of objects selectedĤ Difference between Permutation and Combination NPr = n! / (n-r)! where n is the total number of objects and r is the number of objects selected Selecting 4 books from a shelf without considering their order Order matters, and the arrangement of members is importantĪrranging 4 books on a shelf in different orders Order matters and the arrangement of members is important Permutation involves arranging a set of objects in a particular order, while combination involves selecting a subset of objects from a larger set without regard to order.
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