Out of 8 students, 4 of which are men and the rest women 4 students are selected at random. What is the probability that men equal women?

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justaguide | College Teacher | (Level 2) Distinguished Educator

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There are 8 students in total of which 4 are men and the rest women. When 4 students are randomly picked from this group, the probability that the number of men equals the number of women has to be determined.

The desired probability is given by: (number of favorable events)/(total number of events)

If the number of men and women selected is equal, 2 men out of the four is selected and 2 women out of the 4 is selected. This can be done in C(4, 2)*C(4,2) = 6*6 = 36 ways. The number of ways of selecting 4 students from a group of 8 is C(8, 4) = 70

This gives a probability of 36/70 that an equal number of men and women are selected.

The probability that the random sample of 4 has an equal number of men and women is 18/35.

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