Question 1095712
With 7+6=13 people, you can form {{{13*12*11*10/(2*3*4)}}} committees of 4 people.
Among those there are the only {{{7*6*5*4/(2*3*4)}}} made of all men,
and the only {{{6*5*4*3/(2*3*4)}}} made of all women.
The other committees have at least one person of each gender.
Those are
{{{(13*12*11*10-7*6*5*4-6*5*4*3)/(2*3*4)}}}={{{(13*4*3*11*5*2-(6*5*4)(7+3))/(2*3*4)}}}={{{(13*11*6*5*4-6*5*4*11)/(2*3*4)}}}={{{(13*11-10)*(6*5*4)/(2*3*4)=(143-10)*6*5*4/(2*3*4)=133*6*5*4/(2*3*4)}}}
of the total {{{13*12*11*10/(2*3*4)=13*3*4*11*5*2/(2*3*4)=13*11*6*5*4/(2*3*4)}}}={{143*6*5*4/(2*3*4}}} .
The probability is the ratio of those two quantities,
{{{133*6*5*4/(143*6*5*4)=highlight(133/143)}}} .
 
If you got {{{139/143}}} the mistake was that
{{{13*12*11*10-7*6*5*4-3*6*5*4}}}
is equal to{{{13*12*11*10-(7*6*5*4+3*6*5*4)=13*12*11*10-(7+3)*6*5*4}}}
and not to {{{13*12*11*10-(7-3)*6*5*4}}} .