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!

Each practice test/flash card set has 50 randomly selected questions from a bank of over 500. You'll get a new set of questions each time!

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If n = 6 and r = 2, how many combinations can be formed?

The correct answer is: 15

To determine how many combinations can be formed with $ n = 6 $ and $ r = 2 $, you can use the combinations formula, which is given by: \[ C(n, r) = \frac{n!}{r!(n - r)!} \] In this case: - $ n $ represents the total number of items, which is 6. - $ r $ represents the number of items to choose, which is 2. Substituting the values into the formula, we get: \[ C(6, 2) = \frac{6!}{2!(6 - 2)!} \] \[ = \frac{6!}{2! \cdot 4!} \] Now, let's break down $ 6! $: \[ 6! = 6 \times 5 \times 4! \] So the calculation simplifies to: \[ C(6, 2) = \frac{6 \times 5 \times 4!}{2! \times 4!} \] The $ 4! $ in the numerator and denominator cancels out: \[ = \frac{6 \times