In a business school case competition, the top three teams receive cash prizes of $1000, $ 2000, and $ 3000. while remaining teams are not ranked and do not receive any prizes, there are 6 participating teams, named A, B, C, D, E, F. If team A wins one of the prizes, team B wins also one of the prizes. How many outcomes of the competition are possible ? Choices
A) 18 B) 28 C) 36 D) 84 E) 120
if team A wins one of the prizes, team B wins also one of the prizes". Consider following cases:   A wins one of the prizes, then B must also win one of the prizes, and in this case we can have 4 triplets: {ABC}, {ABD}, {ABE}, {ABF}. Each triplet can be arranged in 3!=6 ways. Hence in the case when A wins one of the prizes  4*6= 
<gadget id="calculator"> 4*6</gadget>
<output>24</output>
24 arrangements are possible.   A does NOT win one of the prizes, then three winners must be from other 5 teams. 3 winners out of 5 (B, C, D, E, F) teams can be chosen in C35=10C53=10 ways and each case (for example {CDE}) can be arranged in 3!=6 ways, hence in the case when A does NOT win one of the prizes 10*6= 
<gadget id="calculator">10*6</gadget>
<output>60</output>
60 arrangements are possible.   Total= 24+60= 
<gadget id="calculator">24+60</gadget>
<output>84</output>
84.   Answer: 84.
<result>D</result>
In a business school case competition, the top three teams receive cash prizes of $1000, $ 2000, and $ 3000. while remaining teams are not ranked and do not receive any prizes, there are 6 participating teams, named A, B, C, D, E, F. If team A wins one of the prizes, team B wins also one of the prizes. How many outcomes of the competition are possible ?