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A nickel, a dime, and 2 quarters are arranged along a side

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Manager
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Status: Still Struggling
Joined: 02 Nov 2010
Posts: 139
Location: India
GMAT Date: 10-15-2011
GPA: 3.71
WE: Information Technology (Computer Software)
Followers: 5

Kudos [?]: 13 [0], given: 8

A nickel, a dime, and 2 quarters are arranged along a side [#permalink] New post 03 Nov 2010, 04:21
Hi guys...
i had a problem and needed an insight on the same:

A nickel, a dime, and 2 quarters are arranged along a side of the table. if the quarter and the dime have to face heads up and nickel can face either heads up or tails up, how many different arrangements of coins are possible?

The answer says :(4!/2!) * 2!

Can somebody please explain me how to arrive to this ans?

Thanks in advance..
_________________

Appreciation in KUDOS please!
Knewton Free Test 10/03 - 710 (49/37)
Princeton Free Test 10/08 - 610 (44/31)
Kaplan Test 1- 10/10 - 630
Veritas Prep- 10/11 - 630 (42/37)
MGMAT 1 - 10/12 - 680 (45/34)

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Kudos [?]: 25043 [0], given: 2702

Re: A nickel, a dime, and 2 quarters [#permalink] New post 03 Nov 2010, 06:29
Expert's post
krishnasty wrote:
Hi guys...
i had a problem and needed an insight on the same:

A nickel, a dime, and 2 quarters are arranged along a side of the table. if the quarter and the dime have to face heads up and nickel can face either heads up or tails up, how many different arrangements of coins are possible?

The answer says :(4!/2!) * 2!

Can somebody please explain me how to arrive to this ans?

Thanks in advance..


Welcome to Gmat Club.

Please read and follow: how-to-improve-the-forum-search-function-for-others-99451.html

So please:
Provide answer choices for PS questions.
Post new questions in a separate thread.


As for your question:

THEORY.
Permutations of n things of which P_1 are alike of one kind, P_2 are alike of second kind, P_3 are alike of third kind ... P_r are alike of r_{th} kind such that: P_1+P_2+P_3+..+P_r=n is:

\frac{n!}{P_1!*P_2!*P_3!*...*P_r!}.

For example number of permutation of the letters of the word "gmatclub" is 8! as there are 8 DISTINCT letters in this word.

Number of permutation of the letters of the word "google" is \frac{6!}{2!2!}, as there are 6 letters out of which "g" and "o" are represented twice.

Number of permutation of 9 balls out of which 4 are red, 3 green and 2 blue, would be \frac{9!}{4!3!2!}.

So, # of arrangements of a nickel, a dime, and 2 quarters, or arrangements of 4 letters NDQQ out of which 2 Q's appear twice will be \frac{4!}{2!}. Next, as nickel can face either heads up or tails up then we should multiple this number by 2, so finally we'll get: \frac{4!}{2!}*2.

Hope it's clear.
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Manager
Manager
User avatar
Status: Still Struggling
Joined: 02 Nov 2010
Posts: 139
Location: India
GMAT Date: 10-15-2011
GPA: 3.71
WE: Information Technology (Computer Software)
Followers: 5

Kudos [?]: 13 [0], given: 8

Re: A nickel, a dime, and 2 quarters [#permalink] New post 03 Nov 2010, 10:31
thanks a lot...
cleared the concept quite well!!
_________________

Appreciation in KUDOS please!
Knewton Free Test 10/03 - 710 (49/37)
Princeton Free Test 10/08 - 610 (44/31)
Kaplan Test 1- 10/10 - 630
Veritas Prep- 10/11 - 630 (42/37)
MGMAT 1 - 10/12 - 680 (45/34)

Re: A nickel, a dime, and 2 quarters   [#permalink] 03 Nov 2010, 10:31
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A nickel, a dime, and 2 quarters are arranged along a side

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