Graduate Management Admission Test (GMAT) Practice Test

What does the combination symbol ⁶C₁ represent?

1. Choice of 1 from 6 items

2. 6 factorial

3. Sum of 6 items

4. Number of ways to arrange 6 items

The correct answer is: Choice of 1 from 6 items

The combination symbol ⁶C₁ represents the number of ways to choose 1 item from a total of 6 distinct items. This is a fundamental concept in combinatorics, where the notation ⁶C₁ specifically indicates a combination without regard to the order of selection. In mathematical terms, combinations are calculated using the formula nCr = n! / [r!(n - r)!], where n is the total number of items, r is the number of items to choose, and "!" denotes factorial, the product of all positive integers up to that number. For ⁶C₁, it translates to 6! / [1!(6 - 1)!], which simplifies to 6 / 1 = 6. This outcome reflects the fact that you can pick any one of the six items, resulting in a total of six distinct choices. The other options, while related to mathematical concepts, do not accurately describe what ⁶C₁ represents. For example, 6 factorial pertains to the total number of ways to arrange 6 items, which is not the same as selecting a subset of those items.