If your class has 10 males and 14 females in it, how many different committees consisting of 4 males and 4 females may be chosen.
(10 choose 4)*(14 choose 4)
The general formula for n choose k is (n!)/(k!*(n-k)!).
To find the number of different committees consisting of 4 males and 4 females that may be chosen from a class with 10 males and 14 females, we can use the concept of combinations.
First, we need to determine the number of ways to choose 4 males from a group of 10. This can be calculated using the formula for combinations:
C(10, 4) = 10! / (4! * (10-4)!) = 10! / (4! * 6!) = (10 * 9 * 8 * 7) / (4 * 3 * 2 * 1) = 210.
Similarly, we need to determine the number of ways to choose 4 females from a group of 14. This can be calculated using the same formula for combinations:
C(14, 4) = 14! / (4! * (14-4)!) = 14! / (4! * 10!) = (14 * 13 * 12 * 11) / (4 * 3 * 2 * 1) = 1001.
Now, to find the total number of different committees consisting of 4 males and 4 females, we multiply the number of ways to choose males and females:
Total number of committees = C(10, 4) * C(14, 4) = 210 * 1001 = 210,210.
Therefore, there are 210,210 different committees consisting of 4 males and 4 females that may be chosen from the given class.