Question 1100877
<br>For the exact question that you asked, the probability is zero, because it is impossible for ANY two people to be chosen for one office.<br>
I assume, then, that what you really meant to ask is the probability that members of the debate team are chosen for 2 of the 4 offices.<br>
In that case, you are choosing 4 of the 14 to be officers; and they must include 2 of the 6 members of the debate tean and 2 of the 8 others.  The probability is then<br>
{{{(C(6,2)*C(8,2))/C(14,4) = (15*28)/1001 = 15*4/143 = 60/143}}}