FTCE Professional Education Practice Exam

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What is the formula for calculating permutations?

nCr = n!/(n-r)r!
nPr = n!/(n-r)!
n! = n(n-1)(n-2)...
All of the above

The correct answer is: nPr = n!/(n-r)!

The formula for calculating permutations is given as nPr = n!/(n-r)!. This formula is utilized when you want to determine the number of ways to arrange r items chosen from a total of n distinct items, where the order of the arrangement matters. In this context, the factorial notation (n!) represents the product of all positive integers up to n. The significance of the (n-r)! in the denominator accounts for the combinations that are not included in the arrangement, effectively cancelling out the arrangements of the remaining items after selecting the r items. This calculation is particularly crucial in scenarios like competition rankings or lineup arrangements where the sequence significantly alters the outcome. Other choices provided are different formulas relevant to combinations or factorial calculations but do not represent the correct formula for permutations specifically. Thus, selection of the correct formula is fundamental for accurately determining arrangements in problems involving permutations.