suppose 15 countries compete in an olympic event. gold, and silver,and bronze medals are awarded. how many different arrangements of winners are there if no country wins more than one medal in this event? show the work. thanks.
15 countries can get the gold
14 countries can get the silver
13 countries can get the bronze
15*14*13
By the formula:
Permutations= 15! /(15-3)!
To determine the number of different arrangements of winners in this scenario, we need to consider the number of choices for each medal.
For the gold medal, any of the 15 countries can win.
After the gold medal is awarded, there are now 14 countries left to choose from for the silver medal.
Similarly, after the gold and silver medals are awarded, there are 13 countries left to choose from for the bronze medal.
Therefore, we can find the total number of arrangements by multiplying the number of choices for each medal:
Total number of arrangements = (number of choices for gold medal) * (number of choices for silver medal) * (number of choices for bronze medal)
= 15 * 14 * 13
= 2730
Hence, there are 2730 different arrangements of winners in this Olympic event if no country wins more than one medal.