In a 4 person race, medals are awarded to the fastest 3 runners. The first-place runner receives a gold medal, the second-place runner receives a silver medal, and the third-place runner receives a bronze medal. In the event of a tie, the tied runners receive the same color medal. (For example, if there is a two-way tie for first-place, the top two runners receive gold medals, the next-fastest runner receives a silver medal, and no bronze medal is awarded). Assuming that exactly three medals are awarded, and that the three medal winners stand together with their medals to form a victory circle, how many different victory circles are possible? Pick.
A) 24	B) 52	C) 96	D) 144	E) 648
Gold can be awarded in 4 ways, then silver can be awarded in 3 ways and Bronze in 2 ways.   therefore the total number of ways are :   4*3*2= 
<gadget id="calculator">  4*3*2</gadget>
<output>24</output>
24ways of awarding the medals and the same number of ways of forming the circle.   This is when there is no tie. And if there is tie, for example all three receive the GOLD or the Silver or the Bronze, then there are 4 more cases. which implies 24*4= 
<gadget id="calculator">24*4</gadget>
<output>96</output>
96. ANS:96
<result>C</result>
In a 4 person race, medals are awarded to the fastest 3 runners. The first-place runner receives a gold medal, the second-place runner receives a silver medal, and the third-place runner receives a bronze medal. In the event of a tie, the tied runners receive the same color medal. (For example, if there is a two-way tie for first-place, the top two runners receive gold medals, the next-fastest runner receives a silver medal, and no bronze medal is awarded). Assuming that exactly three medals are awarded, and that the three medal winners stand together with their medals to form a victory circle, how many different victory circles are possible?