There is a 100% or #1/1# chance a man or woman is selected for the first committee position. (Note: if the question was what is the probability the committee is made up of all women for example, the probability of the first selection would be #50%# or #5/10#
Let us say a person of #x# gender is selected.
There are now #9# people to select the next candidate from. Of these #9# people #4# of them are of gender #x#. Therefore, there is a #4/9# or #44.bar4%# chance a person of gender #x# will be selected.
If another person of gender #x# is in fact selected, there are now #8# people to select the last candidate from. Of these #8# people #3# of them are of gender #x#. Therefore, there is a #3/8# or #37.54%# chance a person of gender #x# will be selected.
Therefore, the probability of having a committee of all men OR all women is:
#1/1 xx 4/9 xx 3/8 = (1 xx 4 xx 3)/(1 xx 9 xx 8) = 12/72 = 1/6 " or "16.bar6%#
