FTCE General Knowledge Math Practice Test

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Prepare for the FTCE General Knowledge Math Test with interactive quizzes and detailed explanations. This resource will enhance your math skills and boost your confidence before the exam. Conquer the test and excel in your teaching career!

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Which expression represents the number of ways to choose r items from n items?

nPr
nCr
nCr=n!/((n-r)!*r!)
n!/(n-r)

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

The expression that represents the number of ways to choose r items from n items is commonly denoted as nCr, which stands for combinations. This notation indicates that the order of selection does not matter, which is essential when discussing the concept of combinations. The formula given in option C, nCr = n! / ((n-r)! * r!), accurately captures this idea. In this formula, n! (n factorial) is the total number of ways to arrange n items, while the division by (n-r)! accounts for the arrangements of the remaining n-r items that are not selected. Furthermore, the r! in the denominator adjusts for the fact that the order in which the r items are chosen does not matter, since any arrangement of those r items represents the same combination. Thus, option C succinctly describes how to calculate combinations, reinforcing the distinction between combinations and permutations, where order does matter. This makes it suited for solving problems that involve selecting items without regard to the sequence of those selections.