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29 Apr 2021, 07:00
Kudos
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
71% (02:17) correct
29%
(02:36)
wrong
based on 62
sessions
History
Date
Time
Result
Not Attempted Yet
What is the number of different 8-letter words ending and beginning with a consonant which can be made out of the letters of the word EQUATION ?
(A) 5200
(B) 4320
(C) 3000
(D) 1295
(E) 1000
(A) 5200
(B) 4320
(C) 3000
(D) 1295
(E) 1000
29 Apr 2021, 07:20
Kudos
Bookmarks
Bunuel
Take the task of seating the 8 letters and break it into stages.
We’ll begin with the most restrictive stages.
Stage 1: Choose a consonant for the 1st letter
There are 3 consonants to choose from (Q, T and N)
So, we can complete stage 1 in 3 ways
Stage 2: Choose a consonant for the 8th letter
There are 2 consonants remaining to choose from (since we already used a consonant in stage 1)
So we can complete stage 2 in 2 ways
We now have 6 spaces and 6 letters remaining.
Stage 3: Choose a letter for the 2nd position
We can do this in 6 ways
Stage 4: Choose a letter for the 3rd position
We can do this in 5 ways
Stage 5: We can choose a letter for the 4th position in 4 ways
Stage 6: We can choose a letter for the 5th position in 3 ways
Stage 7: We can choose a letter for the 6th position in 2 ways
Stage 8: We can choose a letter for the 7th position in 1 way
By the Fundamental Counting Principle (FCP), we can complete all 8 stages (and thus arrange all 8 letters) in (3)(2)(6)(5)(4)(3)(2)(1) ways (= 4320 ways)
Answer: B
Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. So, be sure to learn it.
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General Discussion
29 Apr 2021, 11:48
Kudos
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Answer = 4320 (B)
There are 8 spaces of which 5 are consonants and the rest 3 are vowels.
The first and the 8th space can be filled in 3P2 Ways = 6
The rest 6 spaces need to be filled by the remaining vowel + 5 consonants. This can be done in 6! ways or 6P6 ways.
Thus, total ways = 6 * 6!
Which equals 4320
There are 8 spaces of which 5 are consonants and the rest 3 are vowels.
The first and the 8th space can be filled in 3P2 Ways = 6
The rest 6 spaces need to be filled by the remaining vowel + 5 consonants. This can be done in 6! ways or 6P6 ways.
Thus, total ways = 6 * 6!
Which equals 4320
