# A committee of two persons is selected from 2 men and 2 women.What is the probabality that the committee will have 1) at least one man 2)at most one man What is the difference betwnn these 2 and also i need solotion for both

the number of men =2 the number of woman = 2.
(i) at least one man : at least one man means either committee has one man or it has two man.
the probability of at least one man = 1- probability of no man
i.e. we will calculate the probability that committee has no man and will subtract it from 1
$=1-\frac{{}^{2}C_{2}}{{}^{4}C_{2}}$
$=1-\frac{1}{6}\phantom{\rule{0ex}{0ex}}=\frac{5}{6}$
(ii) at most one men = either committee has one man or no man.
case I : committee has one man = $\frac{{}^{2}C_{1}*{}^{2}C_{1}}{{}^{4}C_{2}}=\frac{2*2}{6}=\frac{2}{3}$
case II: committee has no man = $\frac{{}^{2}C_{2}}{{}^{4}C_{2}}=\frac{1}{6}$
thus the probability that committee has at most one man
$=\frac{2}{3}+\frac{1}{6}\phantom{\rule{0ex}{0ex}}=\frac{4+1}{6}\phantom{\rule{0ex}{0ex}}=\frac{5}{6}$

hope this helps you

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