Graduate Management Admission Test (GMAT) Practice Test

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What does ⁶P₆ represent?

6! (720)
6 choose 5
6 factorial divided by 6
The number of permutations of 6 items

The correct answer is: 6! (720)

The notation ⁶P₆ is used to denote the number of permutations of 6 items taken 6 at a time. This represents the total number of ways to arrange 6 distinct objects in order, where all objects are used. To understand why this is associated with the answer provided, consider that the formula for permutations is given by nPr = n! / (n - r)!. In this case, both n and r are 6, so we apply the formula: ⁶P₆ = 6! / (6 - 6)! = 6! / 0! Since 0! is defined as 1, this simplifies to just 6!. The factorial of 6 (6!) is equal to 720, which directly correlates with the correct option stating 6! (720). Therefore, the correct interpretation of ⁶P₆ is indeed the total number of ways to arrange all 6 items, leading to the conclusion that it represents 720 distinct arrangements.