Combinations

We need to calculate and .

Step 1: Calculate the number of ways to form the committee with at least 6 males. The possible cases are: - 6 males and 5 females: - 7 males and 4 females: - 8 males and 3 females: Thus, the total number of ways to form the committee with at least 6 males is:

Step 2: Calculate the number of ways to form the committee with at least 3 females. The possible cases are: - 8 males and 3 females: - 7 males and 4 females: - 6 males and 5 females: Thus, the total number of ways to form the committee with at least 3 females is:

Step 3: Conclusion. Since both and are 78, the correct answer is .