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# A certain jewelry store sells customized rings in which

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Manager
Joined: 02 Jul 2004
Posts: 51
A certain jewelry store sells customized rings in which   [#permalink]

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15 Oct 2004, 13:21
00:00

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 12 sessions

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A certain jewelry store sells customized rings in which
three gemstones selected by the customer are set in
a straight row along the band of the ring. If exactly
5 different types of gemstones are available, and if
at least two of the gemstones in any given ring must
be different, how many different rings are possible?

(a) 20
(b) 60
(c) 90
(d) 120
(e) 210

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Senior Manager
Joined: 19 May 2004
Posts: 289

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15 Oct 2004, 14:18
Total ways: 5^3 = 125.
Unwanted: 5. (All the same)
125 - 5 = 120
Manager
Joined: 02 Jul 2004
Posts: 51

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15 Oct 2004, 14:26
Thats correct ...
OA is D

When I went to work the problem I kept trying to do

5 possibilities for 1st stone
5 possibilities for 2nd stone
4 possibilities for 3rd stone

or 5*5*4 = 100.

I can see that this is not quite right (for one reason need to divide out identical cases), however can someone please explain why this method is wrong and, if possible, what it's trying to calculate?

Thanks
Senior Manager
Joined: 19 May 2004
Posts: 289

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15 Oct 2004, 17:24
1
tyagel, It is more complicated this way. You didn't count all the options.

There are 2 options:
1) All different = 5*4*3 = 60
+
2) 2 Equal, 1 Different = 5C2 * 2 * 3C2 = 60.

60 + 60 = 120.

Let me explain the second one:
5C2 : Pick 2 stones out of 5 ,
2 : Choose 1 of those two colors again.
3C2 : Pick two places for the identical colors, order doesn't matter.
Manager
Joined: 18 Sep 2004
Posts: 144
Location: Dallas, TX

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16 Oct 2004, 00:08
# all 3 different 5P3 = 5*4*3 = 60

# only 2 are same and 1 different (think of the two same as one) 4P2 = 12

There are 5 different stones that can be group together to form 2 same = 5 * 12

60 + (5*12) = 60+60 120 ways.
Manager
Joined: 02 Jul 2004
Posts: 51

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16 Oct 2004, 07:17
Ok now I understand ...

Thanks for the help!

A slightly different way (although pretty much same a Dookie's) is

5P2*3C2

The first is a permutation since order can be considered to determine which color gets two.
Non-Human User
Joined: 09 Sep 2013
Posts: 10166
Re: A certain jewelry store sells customized rings in which   [#permalink]

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02 Feb 2018, 14:34
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Re: A certain jewelry store sells customized rings in which   [#permalink] 02 Feb 2018, 14:34
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