To find the number of different combinations of two men and two women that can be chosen from a choir consisting of 17 men and 26 women, we can use the concept of combinations.
The number of combinations can be calculated using the formula for combinations, which is given by:
C(n, r) = n! / (r!(n-r)!)
where n is the total number of individuals (men and women) and r is the number of individuals to be chosen (in this case, 2 men and 2 women).
Given:
Number of men = 17
Number of women = 26
Number of men to be chosen = 2
Number of women to be chosen = 2
Using the formula for combinations:
C(17, 2) = 17! / (2!(17-2)!) = (17 * 16) / (2 * 1) = 136 / 2 = 68
C(26, 2) = 26! / (2!(26-2)!) = (26 * 25) / (2 * 1) = 650 / 2 = 325
To find the total number of different combinations, we multiply the number of combinations for men and women together:
Total combinations = C(17, 2) * C(26, 2) = 68 * 325 = 22,100
Therefore, there are 22,100 different combinations of two men and two women that can be chosen from the choir.