Graduate Management Admission Test (GMAT) Practice Test

Is ⁶C₁ equal to ⁶P₁?

1. Yes, equals 6

2. No

3. Yes, equals 1

4. Only for larger numbers

The correct answer is: Yes, equals 6

To understand whether ⁶C₁ is equal to ⁶P₁, it's crucial to look at what these notations represent. ⁶C₁ denotes the number of combinations of 6 items taken 1 at a time. The formula for combinations is given by: \[ ⁿCᵣ = \frac{n!}{r!(n-r)!} \] In this case, we have: \[ ⁶C₁ = \frac{6!}{1!(6-1)!} = \frac{6!}{1! \times 5!} = \frac{6 \times 5!}{1 \times 5!} = 6 \] This means there are 6 ways to choose 1 item from a set of 6. ⁶P₁ represents the number of permutations of 6 items taken 1 at a time. The formula for permutations is given by: \[ ⁿPᵣ = \frac{n!}{(n-r)!} \] For this case, we have: \[ ⁶P₁ = \frac{6!}{(6-1)!} = \frac