A class roster includes 24 male students and 15 female students who are IT majors. If 4 students from the group are selected to represent IT majors at a university meeting, what is the probability 2 will be male and 2 will be female? Please show me how it is derived. One answer I saw has a C in it. I don't know what the "C" stands for.
Hi,Thank you for using JustAnswer.The notation C(n,x) represents the number of ways that "x" items can be selected from a pool of "n" items.The calculation for C(n,x) is:C(n, x) = n! / ( x! * (n - x)! )where the notation n! represents the factorial computation, i.e. n! = n * (n - 1) * (n - 2)...* 2 * 1. For example, 4! = 4 * 3 * 2 * 1 = 24.For this problem, the probability of selecting 2 male and 2 female students is going to be equal to the number of ways that 2 male and 2 female students can be selected, divided by the number of ways that 4 students can be selected, regardless of gender.The total number of students we are selecting from is 24 + 15 = 39.The number of ways to select any 4 from this group is:C(39, 4) = 39! / (4! * (39 - 4)!) = 39! / (4! * 35!) = 82251The number of ways to select 2 males from the 24 male students is:C(24, 2) = 24! / (2! * (24 - 2)!) = 24! / (2! * 22!) = 276The number of ways to select 2 females from the 15 female students is:C(15, 2) = 15! / (2! * (15 - 2)!) = 15! / (2! * 13!) = 105The number of ways to select 2 males AND 2 females is the product of the two above values:C(24, 2) * C(15, 2) = 276 * 105 = 28980So, the probability of selecting 2 males and 2 females to represent IT majors is:P(2 male and 2 female) = 28980 / 82251 = 0.3523Please feel free to ask if you have any questions about this solution. I will be happy to explain anything that is unclear.Thanks,Ryan
Experience: B.S. in Civil Engineering