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Combo/Perm

by gmatusa2010 » Sat Dec 11, 2010 6:03 am
20. A jewelry store sells customized rings in which 3 gems selected by the customer are set in a straight row along the band of the ring. If exactly 5 different gems are available and if at least 2 gems in any given ring must be different, how many different rings are possible?


20
60
90
120
210

Is this problem not specific enough? How do you know from the question that order doesn't matter. It doesnt define what different means here. It's not difficult, if you try 1 method and it doesn't have an answer you try order matters. But is this a realistic gmat problem where they make you do that?
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by Rahul@gurome » Sat Dec 11, 2010 6:31 am
gmatusa2010 wrote:20. A jewelry store sells customized rings in which 3 gems selected by the customer are set in a straight row along the band of the ring. If exactly 5 different gems are available and if at least 2 gems in any given ring must be different, how many different rings are possible?
  • 20
    60
    90
    120
    210
The question asks for number of possible rings with at least 2 gems are different. Now what does that mean? This means the ring may contain all three different gems or exactly two different gems. Now exactly two different gems is equivalent to exactly two same gems. Because exactly two gems are different means the third one must be same as one of them.

Number of possible rings with at least 2 gems are different = (Number of possible rings with all the three gems are different + Number of possible rings with exactly two gems are different) = Number of possible rings in which all the gems are not same = (Total number of possible rings - Number of possible rings with all the gems same) = (5*5*5 - 5) = 120

The correct answer is D.
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