Melanie's classes can be arranged in 24 ways, found using the permutation 4P4.
What is Permutation?
The act of organizing all the components of a set into some sequence or order is known as permutation. Permuting, in other words, is the act of reordering the components of a set that has previously been sorted.
A permutation is the selection of r items from a collection of n items without replacement, with the order of the items being significant.
nPr = (n!) / (n-r)!
What is a Combination?
The combination is a method of picking elements from a collection in which the order of selection is irrelevant (unlike permutations).
A combination is a selection of r items from a collection of n items with no replacements and no regard for order.
nCr = (n!)/{(r!)((n-r)!)}
How do we solve the given question?
We are informed that Melanie is taking four classes this semester: American History, Algebra 2, English 2, and Environmental Science.
We are asked to find out the number of ways in which Melanie's classes can be arranged.
To find the number of arrangements, we will use permutation here as the order of selection matters. Our sample size, n = 4, and the number of selections we need to make, r = 4.
We will use the formula: nPr = (n!) / (n-r)!
∴ 4P4 = (4!)/(4-4)! = 4!/0! = 4!/1 = 4! = 1*2*3*4 = 24. (∵ 0! = 1)
∴ Melanie's classes can be arranged in 24 ways, found using the permutation 4P4.
Learn more about permutations and combinations at
https://brainly.com/question/4658834
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