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13 Jun 2018, 00:07
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
58% (02:07) correct
42%
(02:06)
wrong
based on 104
sessions
History
Date
Time
Result
Not Attempted Yet
A certain jewelry store sells customized pendants in which three gemstones selected by the customer are set in a straight row down the center of the pendant. If exactly 5 different types of the gemstone are available, and if at least two of the gemstones in any given pendant must be different, how many different pendants are possible?
A. 20
B. 60
C. 90
D. 120
E. 210
A. 20
B. 60
C. 90
D. 120
E. 210
Given:
Three stones are to be placed in the pendant and atleast 2 of them should be different.
So there are two possible ways:
1. 2 stones are different:
of the given 5 stones 2 can be selected by
5C2 = 10 ways. In this 2 stones are of the same gem and the other one is different. The one different gem can be selected by 2C1 = 2 ways
Hence this can be arranged in 10*2*(3!/2!) = 60 ways
2. All 3 stones are different:
this can be selected in 5C3 = 10 ways.
This can be arranged in 10*(3!) = 60 ways.
Total possibilities = 60 + 60 = 120.
OA - D
Three stones are to be placed in the pendant and atleast 2 of them should be different.
So there are two possible ways:
1. 2 stones are different:
of the given 5 stones 2 can be selected by
5C2 = 10 ways. In this 2 stones are of the same gem and the other one is different. The one different gem can be selected by 2C1 = 2 ways
Hence this can be arranged in 10*2*(3!/2!) = 60 ways
2. All 3 stones are different:
this can be selected in 5C3 = 10 ways.
This can be arranged in 10*(3!) = 60 ways.
Total possibilities = 60 + 60 = 120.
OA - D
13 Jun 2018, 00:26
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Solution
Given:
- • 5 different types of gemstones are available, out of which 3 needs to be chosen
• At least two gemstones must be different
To find:
- • Number of pendants possible to customize
Approach and Working:
As we have to choose pendants ensuring at least two of gemstones are different, we have the following cases and their corresponding choices:
- • All 3 gemstones are different = \(^5C_3 * 3! = 10 * 6 = 60\)
• Exactly 2 types of gemstones are chosen = \(^5C_2 * ^2C_1 * \frac{3!}{2!} = 10 * 2 * 3 = 60\)
Therefore, the number of different pendants possible = 60 + 60 = 120
Hence, the correct answer is option D.
Answer: D
