Question 870469
There is a group of seven women and nine men, if they plan to make a committee of 5 with at least one woman how many possibilities are there? 
<pre>
{{{(matrix(10,1,

Number, of,Committees,of,5,with,at,least,one,woman))}}} {{{""=""}}} {{{(matrix(7,1,

Number, of,all, possible,Committees,of,5))}}}{{{""-""}}}{{{(matrix(11,1,

Number,of,Committees,of,5,with,NO,women,"i.e.",all,men))}}} {{{""=""}}} {{{"C(16,5)"}}}{{{""-""}}}{{{"C(9,5)"}}} {{{""=""}}} {{{4368-126}}} {{{""=""}}} {{{4242}}}.

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</pre>
at least one man and one woman?<pre>
{{{(matrix(13,1,
Number, of,Committees,of,5,with,at,least,one,man,and,one,woman))}}} {{{""=""}}} {{{(matrix(7,1,

Number, of,all, possible,Committees,of,5))}}}{{{""-""}}}{{{(matrix(11,1,

Number,of,Committees,of,5,with,NO,women,"i.e.",all,men))}}}{{{""-""}}}{{{(matrix(11,1,Number,of,Committees,of,5,with,NO,men,"i.e.",all,women))}}} {{{""=""}}} {{{"C(16,5)"}}}{{{""-""}}}{{{"C(9,5)"}}}{{{""-""}}}{{{"C(7,5)"}}} {{{""=""}}} {{{4368-126-21}}} {{{""=""}}} {{{4221}}}.

[Notice: for the second one, we could have just subtracted 21 from the
answer to the the first one).

Edwin</pre>