Graduate Management Admission Test (GMAT) Practice Test

Are the values of ⁶C₅ and ⁶P₅ equal?

1. Yes

2. No

3. It depends on the context

4. Only under certain conditions

The correct answer is: No

To determine whether the values of \( \binom{6}{5} \) (the combination of 6 items taken 5 at a time) and \( P(6, 5) \) (the permutation of 6 items taken 5 at a time) are equal, it's important to understand the definitions and calculations of combinations and permutations. The value of \( \binom{6}{5} \) is calculated as follows: \[ \binom{n}{r} = \frac{n!}{r!(n-r)!} \] For \( \binom{6}{5} \): \[ \binom{6}{5} = \frac{6!}{5!(6-5)!} = \frac{6!}{5! \cdot 1!} = \frac{6 \times 5!}{5! \cdot 1} = 6 \] This means there are 6 ways to choose 5 items out of 6. On the other hand, the value of \( P(6,5) \) is calculated as follows: \[ P(n, r) = \frac{n!}{(n-r)!