Question 1070134
Can't have 1 black button, that means you'd have 8 brown buttons but you only have 7.
.
.
.
Set up a table. 
Let X be the number of black buttons chosen.
Let Y be the number of brown buttons chosen.
.
.
.
*[illustration fr4.JPG].
.
.
.
So sum the last column in the rows from X=2 to X=5,
{{{P=(21+245+735+735)/2002}}}
{{{P=1736/2002}}}
{{{P=124/143}}}