BTGmoderatorDC wrote: ↑

Sun Feb 02, 2020 7:08 pm

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?

A. 10!/7!
B. 10!/(3!7!)
C. 10!/3!
D. 7!/3!
E. 7!/94!3!)

OA A

Source: Manhattan Prep

• The gold medal can be awarded in 10 ways;
• The silver medal can be awarded in 9 ways; since one team already got gold.
• The bronze medal can be awarded in 8 ways; since two teams already got gold and silver.

Total no. of ways = 10*9*8; this can also be written as 10!/7!.

The correct answer: A

Hope this helps!

-Jay
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BTGmoderatorDC wrote: ↑

Sun Feb 02, 2020 7:08 pm

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?

A. 10!/7!
B. 10!/(3!7!)
C. 10!/3!
D. 7!/3!
E. 7!/94!3!)



OA A

Source: Manhattan Prep

Since the order matters (i.e., who gets gold, who gets silver and who gets bronze matters), the number of ways that 3 teams can be chosen from 10 teams is:

10P3 = 10 x 9 x 8 = (10 x 9 x 8 x 7!)/7! = 10!/7!

Answer: A