Question

A class consists of 10 male and 10 female students. if four students are selected at random, without replacement, what if four students are selected at random, without replacement, what is the probability that all four are male

Answer 1

$\displaystyle |\Omega|=\binom{20}{4}=\dfrac{20!}{4!16!}=\dfrac{17\cdot18\cdot19\cdot20}{2\cdot3\cdot4}=4845\\ |A|=\binom{10}{4}=\dfrac{10!}{4!6!}=\dfrac{7\cdot8\cdot9\cdot10}{2\cdot3\cdot4}=210\\\\ P(A)=\dfrac{210}{4845}=\dfrac{14}{323}\approx4.3\%$

Answer 2

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