Medals are to be awarded to three teams in a 10-team competition. If one medal is gold, one medal is silver, and one medal is bronze, how many different ways are there to award the three medals to teams in the competition?  Choose the most appropriate option: A) 10!/7! B) 10!/(3!7!) C) 10!/3! D) 7!/3! E) 7!/94!3!)
Choosing 3 teams out of 10 when order of the teams matters - P310=10!7!   Or: choosing which 3 teams out of 10 will get the medals - C310C103 and arranging them - 3!3!, so total - C310∗3!=10!7!   Or:   1-2-3-4-5-6-7-8-9-10 (teams);   G-S-B-N-N-N-N-N-N-N (GSB - medals, N - no medal);   Permutation of 10 letters out of which 7 N's are identical is 10!7!10!7! (so you'll get 10!7!10!7! different ways of assigning the medals to the teams).   10!/7!nswer: 10!/7!.
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Medals are to be awarded to three teams in a 10-team competition. If one medal is gold, one medal is silver, and one medal is bronze, how many different ways are there to award the three medals to teams in the competition?