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08 May 2020, 09:43
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C
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Difficulty:
95%
(hard)
Question Stats:
47% (03:01) correct
53%
(02:42)
wrong
based on 94
sessions
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All the rearrangements of the word "DEMAND" are written without including any word that has two D's appearing together. If these are arranged alphabetically, what would be the rank of "DEMAND"?
A. 36
B. 42
C. 74
D. 75
E. 86
Are You Up For the Challenge: 700 Level Questions
A. 36
B. 42
C. 74
D. 75
E. 86
Are You Up For the Challenge: 700 Level Questions
08 May 2020, 16:08
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Bunuel
The letters when arranged alphabetically are: A D D E M N
The first sets of words formed would be starting with A: Total such words = 5!/2! = 60
Let us find the number of words where 'DD' appears in the above cases:
Number of arrangements of: A (DD) (E) (M) (N); where A is fixed in the first place => 4! = 24
=> Required number of words starting with A (where the two D's did not appear together) = 60 - 24 = 36 ... (i)
The next set of words would start with D, same as what our word DEMAND starts with.
Of these, the first few words would start with DA. Number of such words: DA (D) (E) (M) (N) => 4! = 24 ... (ii)
Note: there is no scope of DD occurring in this case
Next, we have words that start with DD - but are ignored according to the question.
Next, we have words that start with DE.
Of these, the first few words would start with DEA. Number of such words: DEA (D) (M) (N) => 3! = 6 ... (iii)
Note: there is no scope of DD occurring in this case
Next, we have words that start with DED. Number of such words: DED (A) (M) (N) => 3! = 6 ... (iv)
Note: there is no scope of DD occurring in this case
Next, we have words that start with DEM - same as our required word DEMAND.
Of these, the first few would start with DEMA - same as our word DEMAND
Of these, the first few would start with DEMAD. Number of such words: DEMAD (N) => 1! = 1 ... (v)
Note: there is no scope of DD occurring in this case
The next word would be DEMAND
Number of words that occur before DEMAND = 36 + 24 + 6 + 6 + 1 = 73
Ranking of DEMAND - 74
Answer C
10 May 2020, 18:04
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All the rearrangements of the word "DEMAND" are written without including any word that has two D's appearing together. If these are arranged alphabetically, what would be the rank of "DEMAND"?
WE need to make a list of words arranging alphabetically from ADDEMN to DEMAND.
Starting from A
A- (DDEMN): \(\frac{5!}{2!}= 60\) words in total.
But "DD" cannot be put together.
(DD)(EMN)
--1----234 ---> 4!= 24 times two DDs come together
60 -24 =36 words for when starting with A.
Starting with DA (DEMN)
DA - (DEMN)= 4! = 24 words
Starting with DEA (DMN)
DEA - (DMN)= 3!= 6 words
Starting with DED (AMN)
DED - (AMN)= 3!= 6 words
Starting with DEM (ADN)= 1 word
Starting with DEM (AND)= 1 word
In total, 36 + 24+ 6+ 6+1 +1= 74
Answer (C).
WE need to make a list of words arranging alphabetically from ADDEMN to DEMAND.
Starting from A
A- (DDEMN): \(\frac{5!}{2!}= 60\) words in total.
But "DD" cannot be put together.
(DD)(EMN)
--1----234 ---> 4!= 24 times two DDs come together
60 -24 =36 words for when starting with A.
Starting with DA (DEMN)
DA - (DEMN)= 4! = 24 words
Starting with DEA (DMN)
DEA - (DMN)= 3!= 6 words
Starting with DED (AMN)
DED - (AMN)= 3!= 6 words
Starting with DEM (ADN)= 1 word
Starting with DEM (AND)= 1 word
In total, 36 + 24+ 6+ 6+1 +1= 74
Answer (C).
