Since the problem didn't specify which genre will come first or second, we don't know which of n1,n2, or n3 will get r=3 or 2 or 1, so I understand this way isn't correct, but I'm struggling to understand when to use Permutation rule and when to use simply just multiplication principle.Įxperiment: I assigned random numbers to n1,n2,n3 (n1=5,n2=6, n3=7) and tried both ways and the correct way ( 3! (n1!)(n2!) (n3!)) shows a lot more ways then using the permutation rule.ģ!(5!)(6!)(7!) vs. Permutation(n1 and r=3*Permutation(n2 and r=2)*Permutation(n3=r=1) Permutations - Order Matters The number of ways one can select 2 items from a set of 6, with order mattering, is called the number of permutations of 2 items selected from 6 6×5 30 P62 Example: The final night of the Folklore Festival will feature 3 different bands. We can say the total # of ways to place the CDs and keeping the genres together are: To calculate a permutation, you will need to use the formula n P r n / ( n - r ). P(n,r) represents the number of permutations of n items r at a time. n n(n - 1)(n - 2)(n - 3) (3)(2)(1) Permutations of n items taken r at a time. With 3 objects A, B, and C, there are 6 possible permutations: ABC, ACB. But since the order matters, can we still apply the permutation rule?įor instance, r = 3 since there are 3 ways to order 3 genres. A permutation is a method to calculate the number of events occurring where order matters. Example: How many different ways can 3 students line up to purchase a new textbook reader Solution: n-factorial gives the number of permutations of n items. An arrangement of objects where order matters is called a permutation. MY QUESTION: In this problem, the order matters, but it doesn't specify which genre should come first or second, or third. And because there are 3 different ways to order classical, rock and pop, we want to multiply by 3 factorial. How many ways can we place the CDs on a rack but keep the genres together?īecause there are n1 ways to order classical, n1i (n1 factorial), similarly we have n2i, n3i. This Article will Help you to understand the concept of Permutation in a way that.Problem: You have CDs of which n1= # of classical, n2= # of rocks, n3= # of pop.
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