A nickel, a dime, and 2 identical quarters are arranged

marcodonzelli · **Posted:** Thu Jan 31, 2008 10:22 pm


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A nickel, a dime, and 2 identical quarters are arranged along a side of a table. If the quarters and the dime have to face heads up, while the nickel can face either heads up or tails up, how many different arrangements of coins are possible?
A. 12
B. 24
C. 48
D. 72
E. 96

[Reveal] Spoiler: OA

B

T740qc · **Posted:** Sun Feb 05, 2012 5:14 pm

can somone explain this please? 4!/2! to get to diff ways the coins can be placed taking into acct the repeat in quarters but i don't get the *2! part. Thanks!

Bunuel · **Posted:** Sun Feb 05, 2012 7:42 pm

T740qc wrote:

can somone explain this please? 4!/2! to get to diff ways the coins can be placed taking into acct the repeat in quarters but i don't get the *2! part. Thanks!

Welcome to Gmat Club.

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!}.

BACK TO THE ORIGINAL QUESTION:
A nickel, a dime, and 2 identical quarters are arranged along a side of a table. If the quarters and the dime have to face heads up, while the nickel can face either heads up or tails up, how many different arrangements of coins are possible?
A. 12
B. 24
C. 48
D. 72
E. 96

# 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=24.

Answer: B.

Hope it's clear.

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A nickel, a dime, and 2 identical quarters are arranged

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