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Medals are to be awarded to three teams in a 10-team [#permalink]
02 Oct 2010, 02:54

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Difficulty:

25% (medium)

Question Stats:

58% (01:24) correct
42% (00:36) wrong based on 78 sessions

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!)

Re: medals are to be aworded [#permalink]
02 Oct 2010, 03:46

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anilnandyala wrote:

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!/4! 3!

pls provide answer with explanation

Choosing 3 teams out of 10 when order of the teams matters - \(P^3_{10}=\frac{10!}{7!}\);

Or: choosing which 3 teams out of 10 will get the medals - \(C^3_{10}\) and arranging them - \(3!\), so total - \(C^3_{10}*3!=\frac{10!}{7!}\);

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 \(\frac{10!}{7!}\) (so you'll get \(\frac{10!}{7!}\) different ways of assigning the medals to the teams).

Re: medals are to be aworded [#permalink]
02 Oct 2010, 07:15

anilnandyala wrote:

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!/4! 3!

pls provide answer with explanation

Step 1 : Choose 3 teams out of 10 = C(10,3) Step 2 : Distribute the 3 medals between these = 3!

Answer : C(10,2) * 3! = 10!/7! or (A) _________________

Re: Medals are to be awarded to three teams in a 10-team [#permalink]
19 Aug 2014, 22:44

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