BTGmoderatorDC wrote:In a business school case competition, the top three teams receive cash prizes of $5,000, $3,000, and $2,000, respectively, while the remaining teams are not ranked and do not receive any prizes. There are 6 participating teams, named Team A, Team B, Team C, Team D, Team E, and Team F. If Team A wins one of the prizes, Team B will also win one of the prizes. How many outcomes of the competition are possible?
A. 18
B. 20
C. 54
D. 84
E. 120
Case 1: Team A wins a prize, with the result that Team B must win a prize
Number of prizes that could be won by A = 3.
Number of remaining prizes that could be won by B = 2.
Number of teams that could win the third prize = 4. (Any of the 4 remaining teams.)
To combine these options, we multiply:
3*2*4 = 24.
Case 2: Team A does NOT win a prize
Number of teams that could win the first prize = 5. (Of the 6 teams, any team but A.)
Number of teams that could win the second prize = 4. (Of the 5 remaining teams, any team but A.)
Number of teams that could win the third prize = 3. (Of the 4 remaining teams, any team but A.)
To combine these options, we multiply:
5*4*3 = 60.
Total ways = Case 1 + Case 2 = 24 + 60 = 84.
The correct answer is
D.
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