Graduate Management Admission Test (GMAT) Practice Test

In calculating the probability of tossing 2 heads in 3 coin tosses, what method is applied to find combinations?

1. n! / (k! * (n - k)!)

2. Total outcomes of the coin tosses / favorable outcomes

3. (3! / (2! * 1!)) / (0.5 ^ 3)

4. P(HHT) = 3 * (1/8)

The correct answer is: n! / (k! * (n - k)!)

The correct answer utilizes the concept of combinations to determine how many ways a certain outcome can occur—in this case, the outcome of tossing 2 heads in 3 coin tosses. In any scenario involving a fixed number of trials, the total arrangements of successful outcomes (e.g., heads) can be calculated using the formula n! / (k! * (n - k)!), where n represents the total number of trials, k signifies the number of successful outcomes desired, and the exclamation mark denotes a factorial, which is the product of all positive integers up to that number. For tossing 2 heads in 3 attempts, there are 3 total tosses (n = 3) and we want to find the combinations of 2 heads (k = 2). This calculation represents the different sequences in which 2 heads and 1 tail could occur, such as HHT, HTH, and THH. The value of the combination calculated using this formula gives us the number of favorable outcomes of interest. This method is fundamental in probability calculations that involve distinct outcomes across multiple trials, particularly when order does not matter. In contrast, the other options discuss various methods for probability calculation, but they do not accurately use the principles of