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02 Sep 2020, 22:52
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
48% (01:18) correct
52%
(02:08)
wrong
based on 29
sessions
History
Date
Time
Result
Not Attempted Yet
Using the letters from the word ‘TRAPEZIUM’, how many combinations 5 letters can be formed such that they have exactly 3 consonants?
A)120
B)600
C)3,600
D)4,800
E)7,200
need detail explanation
A)120
B)600
C)3,600
D)4,800
E)7,200
need detail explanation
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02 Sep 2020, 23:00
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There are 5 consonants which can be selected in 5C3 ways , remaining 2 letters will be vowels which are selected in 4C2 ways .There are 5 distinct letters selected as no letter of the word"Trapezium" repeats
The 5 letters selected can be arranged in 5! Ways
Therefore total number of combinations formed =5C3*4C2*5!
=10*6*120
=7200
Posted from my mobile device
The 5 letters selected can be arranged in 5! Ways
Therefore total number of combinations formed =5C3*4C2*5!
=10*6*120
=7200
Posted from my mobile device
03 Sep 2020, 06:45
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kawal27
The right answer is not among the choices. In combinatorics, when someone talks about "combinations", then they specifically mean "sets where order does not matter". It's a word with a precise definition in math. If order matters, you're dealing with a "permutation", not a "combination". You don't need to know these words on actual GMAT questions, but this question is using one of them, and it's using it incorrectly, judging by the answer choices.
We need to pick 3 out of 5 consonants, which we can do in (5)(4)(3)/3! = 10 ways. We need to pick 2 out of 4 vowels, which we can do in (4)(3)/2! = 6 ways. In total, we thus have 10*6 = 60 choices. We should not then arrange our selection in various orders, because the question is asking specifically for "combinations".
I'm assuming we need to pick distinct letters, something else the question needs to be clear about. In general, I'd be wary about using sources for GMAT preparation that misuse basic mathematical terminology.
