Question 1071176
You have 29 people, so the number of possible sets of 12 of them
(the number of possible randomly selected juries) is
{{{(matrix(2,1,29,12))=29*28*"..."*20*19*18/(12*11*10*"..."*3*2)="51,895,936"=3^2*5*7*13*19*23*29}}} ,
combinations of 29 taking 12 at a time.
You can get that from a calculator or some software in your computer,
but it is also relatively easy to use pencil and paper
to get the factored form.
The number of possible sets of 12 males
that can be made from the 17 males in the jury pool is
{{{(matrix(2,1,17,12))=(matrix(2,1,17,5))=17*16*15*14*13/(5*4*3*2)=6188=2^2*7*13*17}}}
As a fraction of the total number of possible randomly selected juries,
that number represents
{{{6188/51895935=2^2*7*13*17/(3^2*5*7*13*19*23*29)=2^2*17/(3^2*5*19*23*29)=highlight(68/570285)}}} .
That is about 0.01%, so it is unlikely to happen by chance.