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

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New post 03 Nov 2010, 05:21
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..
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Re: A nickel, a dime, and 2 quarters [#permalink]

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New post 03 Nov 2010, 07:29
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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

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Provide answer choices for PS questions.
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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
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Status: Still Struggling
Joined: 03 Nov 2010
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GMAT Date: 10-15-2011
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WE: Information Technology (Computer Software)
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Kudos [?]: 62 [0], given: 8

Re: A nickel, a dime, and 2 quarters [#permalink]

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New post 03 Nov 2010, 11:31
thanks a lot...
cleared the concept quite well!!
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Re: A nickel, a dime, and 2 quarters are arranged along a side [#permalink]

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New post 13 Sep 2015, 10:56
shouldnt it be HTHH or HHHH, so 4!/3! +1 = 5
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Re: A nickel, a dime, and 2 quarters are arranged along a side [#permalink]

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New post 14 Sep 2015, 05:27
Expert's post
SahilKataria wrote:
shouldnt it be HTHH or HHHH, so 4!/3! +1 = 5


The number 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: \(\frac{4!}{2!}*2\).
_________________

New to the Math Forum?
Please read this: All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
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Re: A nickel, a dime, and 2 quarters are arranged along a side [#permalink]

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New post 14 Sep 2015, 11:19
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i get ur point,
its like nickel head ort tale or a dime head or a tail, not just a head or a tail ...so definitely more than 5 cases.
Apreciate help, Thank u.
Re: A nickel, a dime, and 2 quarters are arranged along a side   [#permalink] 14 Sep 2015, 11:19
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A nickel, a dime, and 2 quarters are arranged along a side

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