![]() ![]() 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. We use the formula P (n,r) (n)/ ( (n-r)), where is the factorial function, to compute the number of r-permutations on an n-set, i.e., permutations of r symbols taken from a set of n. As per the permutation formula, the permutation. ![]() Permutations are useful to form different words, number arrangements, seating arrangements, and for all the situations involving different arrangements. Permutation(n1 and r=3*Permutation(n2 and r=2)*Permutation(n3=r=1) The permutation formula is used to find the different number of arrangements that can be formed by taking r things from the n available things. We can say the total # of ways to place the CDs and keeping the genres together are: 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. ![]() 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. Problem: You have CDs of which n1= # of classical, n2= # of rocks, n3= # of pop. ![]()
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