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# Medals are to be awarded to three teams in a 10-team

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Manager
Joined: 07 Feb 2010
Posts: 111
Medals are to be awarded to three teams in a 10-team  [#permalink]

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02 Oct 2010, 02:54
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35% (medium)

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60% (00:58) correct 40% (01:03) wrong based on 166 sessions

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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?

A. 10!/7!
B. 10!/(3!7!)
C. 10!/3!
D. 7!/3!
E. 7!/94!3!)
Math Expert
Joined: 02 Sep 2009
Posts: 62619
Re: medals are to be aworded  [#permalink]

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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!

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).

Hope it's clear.
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Re: medals are to be aworded  [#permalink]

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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!

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)
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Manager
Joined: 22 Aug 2008
Posts: 102
Re: medals are to be aworded  [#permalink]

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03 Oct 2010, 02:52
its choosing 3 teams from 10 teams when the order matters
so its 10P3.
the ans is A
Intern
Joined: 10 Jul 2010
Posts: 32
Re: medals are to be aworded  [#permalink]

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03 Oct 2010, 08:44
Hi Bunuel,

Pls tell me if there is anything wrong with my approach...

10C1*9C1*8C1 which comes out to be A
Intern
Joined: 13 Oct 2010
Posts: 1
Re: medals are to be aworded  [#permalink]

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20 Oct 2010, 04:34
I thought the ten choose three formula was (n choose k)= n!/(k!(n-k)!)

Am I over thinking this...
Joined: 27 Jan 2010
Posts: 133
Concentration: Strategy, Other
Re: medals are to be aworded  [#permalink]

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23 Feb 2011, 13:45
georgea wrote:
I thought the ten choose three formula was (n choose k)= n!/(k!(n-k)!)

Am I over thinking this...

Your formula only works when the order does not matter.
When the order matters, as it does in this case, the formula is: (n Permut k)= n!/(n-k)!
Manager
Joined: 07 Jun 2010
Posts: 76
Re: medals are to be aworded  [#permalink]

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23 Feb 2011, 20:51
Agreed, A. I used slot method as order matters
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Re: Medals are to be awarded to three teams in a 10-team  [#permalink]

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08 Feb 2020, 12:19
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!/94!3!)

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!

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Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 9972
Location: United States (CA)
Re: Medals are to be awarded to three teams in a 10-team  [#permalink]

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09 Feb 2020, 05:15
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!/94!3!)

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!

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
197 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Re: Medals are to be awarded to three teams in a 10-team   [#permalink] 09 Feb 2020, 05:15
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