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08 May 2020, 10:25
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B
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Difficulty:
85%
(hard)
Question Stats:
52% (02:14) correct
48%
(02:42)
wrong
based on 187
sessions
History
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In how many ways can letters the word ATTITUDE be rearranged such that no two Ts are adjacent to each other?
A. 1800
B. 2400
C. 3600
D. 4320
E. 6720
Are You Up For the Challenge: 700 Level Questions
A. 1800
B. 2400
C. 3600
D. 4320
E. 6720
Are You Up For the Challenge: 700 Level Questions
09 May 2020, 08:02
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Bunuel
without the Ts, there are 5 other distinct letters: A I U D E
these 5 letters can arrange themselves in 5! or 120 ways
now, to ensure that no two Ts are together, there must be at least one letter between any two Ts . If we represent each of the other letters as X, then the arrangement can be
_X_X_X_X_X_
here the three Ts can take any 3 of the 6 vacant positions, and this will also ensure no two Ts are together
number of ways three positions can be taken out of the six vacant places = 6C3 = 20
hence, total number of ways = 120 x 20 = 2400 (option B)
General Discussion
shameekv1989
GMAT 3: 720 Q50 V38
Posts: 820
08 May 2020, 11:05
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In how many ways can letters the word ATTITUDE be rearranged such that no two Ts are adjacent to each other?
A. 1800
B. 2400
C. 3600
D. 4320
E. 6720
Total arrangements = 8!/3! = 6720 ways
Case I) All the T's are together - 6! = 720 ways
Case II) exactly 2 T's are together
For 1st position - 1 T out of 3 -> 3 ways
For 2nd position - 1 T out of the remaining 2 -> 2 ways
For 3rd position - No T -> 5 ways
For 4th position - Any remaining alphabets -> 5 ways
For 5th position - 4 ways
For 6th position - 3 ways
For 7th position - 2 ways
For 8th position - 1 ways
=> 3*2*5*5*4*3*2*1 = 3600
Therefore total combinations of no T's together = 6720-720-3600 = 2400 ways
Answer - B
A. 1800
B. 2400
C. 3600
D. 4320
E. 6720
Total arrangements = 8!/3! = 6720 ways
Case I) All the T's are together - 6! = 720 ways
Case II) exactly 2 T's are together
For 1st position - 1 T out of 3 -> 3 ways
For 2nd position - 1 T out of the remaining 2 -> 2 ways
For 3rd position - No T -> 5 ways
For 4th position - Any remaining alphabets -> 5 ways
For 5th position - 4 ways
For 6th position - 3 ways
For 7th position - 2 ways
For 8th position - 1 ways
=> 3*2*5*5*4*3*2*1 = 3600
Therefore total combinations of no T's together = 6720-720-3600 = 2400 ways
Answer - B
