Suppose you are choosing 4 people for a job. There are 5 males and 10 females. How would one go about calculating the probability that all 4 people are of the same gender. I started with the basic Combination without repeats formula but quickly understood that this wont work. I assume that combinations are the way to go here?
2026-03-18 10:22:06.1773829326
What is the probability of randomly picking x amount items out of 2 sets, and the x items being of only one set.
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You can still use combination, but in a proper sort of usage. Obviously choosing 4 people out of 15 is possible in $\binom{15}{4}$ ways. If they are all from same gender, they should be all males or females, totally in $\binom{10}{4}+\binom{5}{4}$ different ways. The correct answer would be $$ \binom{10}{4}+\binom{5}{4}\over \binom{15}{4} $$