Graduate Management Admission Test (GMAT) Practice Test

What is the appropriate approach for calculating different combinations or permutations of two distinct groups?

1. Calculate separately and add the results

2. Calculate separately and multiply the results

3. Calculate them together as one group

4. Multiply the results and then divide by two

The correct answer is: Calculate separately and multiply the results

When dealing with combinations or permutations of two distinct groups, the appropriate approach is to calculate separately for each group and then multiply the results. This method is correct due to the fundamental counting principle, which states that if one event can occur in a certain number of ways and a second event can occur independently in a certain number of ways, then the two events can occur in the product of those two numbers of ways. For instance, if one group has three distinct objects and another group has four, the combinations or arrangements of selecting one from the first group and one from the second can be found by multiplying the possible choices from each group: 3 choices from the first group times 4 choices from the second group equals 12 total combinations. Thus, by breaking down the calculation and treating each distinct group separately, you ensure that all possible interactions between the groups are considered, leading to a comprehensive tally of combinations or permutations, which is why this multiplication approach is effective.