ronnie1985 wrote: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
Please explain, how to solve.
Good rings = total possible rings - bad rings.
Total possible rings:
For each of the 3 positions in the ring, any of the 5 gems could be selected.
Number of options for the first position = 5.
Number of options for the second position = 5.
Number of options for the third position = 5.
To combine these options, we multiply:
5*5*5 = 125.
Bad rings:
In a good ring, at least 2 of the gems are different.
Thus, in a bad ring, all 3 gems are the same.
Thus, if the gem types are A, B, C, D and E, there are only 5 bad rings:
AAA, BBB, CCC, DDD, EEE.
Good rings = 125-5 = 120.
The correct answer is
D.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at
[email protected].
Student Review #1
Student Review #2
Student Review #3
