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If n = 6 and r = 2, how many combinations can be formed?
15
12
20
30
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