Graduate Management Admission Test (GMAT) Practice Test

What is the value of ⁶P₀?

1. 0

2. 6

3. 1

4. 720

The correct answer is: 1

To determine the value of \( ⁶P₀ \), we need to understand the notation used, which represents permutations. In general, the formula for permutations is given by: \[ ⁿPₖ = \frac{n!}{(n-k)!} \] where \( n \) is the total number of items to choose from, \( k \) is the number of items to arrange, and \( ! \) denotes factorial, which is the product of all positive integers up to that number. In this specific case, we are calculating \( ⁶P₀ \). Here, \( n \) is 6 (the total number of items), and \( k \) is 0 (the number of items we want to arrange). Plugging these values into the formula, we have: \[ ⁶P₀ = \frac{6!}{(6-0)!} = \frac{6!}{6!} \] Now, since \( 6! \) divided by \( 6! \) equals 1, we find that: \[ ⁶P₀ = 1 \] This means that there is exactly one way to arrange zero items