Graduate Management Admission Test (GMAT) Practice Test

What is the result of calculating 6C4?

1. 10

2. 15

3. 20

4. 30

The correct answer is: 15

To calculate 6C4, which represents the number of combinations of 6 items taken 4 at a time, you can use the combination formula: \[ nCk = \frac{n!}{k!(n-k)!} \] In this case, \( n = 6 \) and \( k = 4 \). Plugging in these values: \[ 6C4 = \frac{6!}{4!(6-4)!} = \frac{6!}{4! \cdot 2!} \] Now, calculating the factorials: - \( 6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 720 \) - \( 4! = 4 \times 3 \times 2 \times 1 = 24 \) - \( 2! = 2 \times 1 = 2 \) Substituting these into the formula: \[ 6C4 = \frac{720}{24 \times 2} = \frac{720}{48} = 15 \] Thus, the correct answer is indeed 15, which corresponds to the choice provided