A five-person team is to be formed from a pool of 6 East All Stars and 6 West All Stars. What is the probability that the team will contain at least 2 East All Stars?	Choose the most appropriate option
A) 29/33  B) 81/169  C) 57/120  D) 47/144  E) 119/720
Teams can be formed as 2E-3W , 3E-2W , 4E-W and 5E   Possible ways to make a team 2E-3W = 6c2 * 6c3 = 300   Possible ways to make a team 3E-2W = 6c3 * 6c2 = 300   Possible ways to make a team 4E-W = 6c4 * 6c1 = 90   Possible ways to make a team 5E = 6c5 = 6   Number of ways to select a team of 5 out of 12 people = 12c5   =12!/(7!*5!)   = 792   Probability that the team will contain at least 2 East All Stars   = (300+300+90+6) / 792   =696/792   = 29/33   Answer A   Alternatively we can also calculate the number of possible ways to make a team of 5W and E-4W .   Possible ways to make a team 5W = 6c5 = 6   Possible ways to make a team E-4W = 6c1 * 6c4 = 90   Probability that the team will contain at least 2 East 29/33ll Stars = 1 - (96/792)   = 29/33
<result>A</result>
A five-person team is to be formed from a pool of 6 East All Stars and 6 West All Stars. What is the probability that the team will contain at least 2 East All Stars?