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 C different victory circles are possible?	Choose the correct answer:
A) 24 B) 52 C) 96 D) 144 E) 648
Possible scenarios are:   1. Gold/Silver/Bronze/No medal (no ties) - 4!=24;   2. Gold/Gold/Silver/No medal - 4!/2!=12;   3. Gold/Silver/Silver/No medal - 4!/2!=12;   4. Gold/Gold/Gold/No medal - 4!/3!=4.   Total:  24+12+12+4= 
<gadget id="calculator"> 24+12+12+4</gadget>
<output>52</output>
52   Answer: 52.
<result>B</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 C different victory circles are possible?