Latest IBM Aptitude Question SOLUTION: If the letters of the word CHASM are rearranged to form 5 letter words such that none of the word repeat and the results arranged in ascending order as in a dictionary what is the

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If the letters of the word CHASM are rearranged to form 5 letter words such that none of the word repeat and the results arranged in ascending order as in a dictionary what is the rank of the word CHASM?

Solution

total words = 120
now rank of CHASM will be
120*(2-1)/5 + 24*(2-1)/4 + 6*(1-1)/3 + 2*(2-1)/2 + 1 = 24 + 6 + 0 + 1 + 1 = 32

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Asked In IBM (12 years ago)

Solved Read Solution (9)

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Read Solution (9) :

Gautam yadav   (11 years ago)

let us rank the letters a-1,c-2,h-3,m-4,s-5
so we hae to acheie the arrangement 23154
there are 24 numbers starting with 1
so 25th letter will be 21345
there will be 6 letter which start with 21
so 30th letter will be 21543
31th will be 23145
and 32nd will be 23154 which is req number

Is this solution Helpfull? Yes (12) | No (2)  

Mathiazhagan  (11 years ago)

Admin Please explain 120*(2-1)/5 + 24*(2-1)/4 + 6*(1-1)/3 + 2*(2-1)/2 + 1

(2-1)/5 ?
(1-1)/3 ?

Is this solution Helpfull? Yes (8) | No (1)  

surbhi  (12 years ago)

32th word is correct

Is this solution Helpfull? Yes (7) | No (1)  

uthra murugesan  (8 years ago)

The 5 letter word can be rearranged in 5!=120 Ways without any of the letters repeating.

The first 24 of these words will start with A.

Then the 25th word will start will CA _ _ _.
The remaining 3 letters can be rearranged in 3!=6 Ways. i.e. 6 words exist that start with CA.

The next word starts with CH and then A, i.e., CHA _ _.
The first of the words will be CHAMS. The next word will be CHASM.

Therefore, the rank of CHASM will be 24+6+2= 32

Is this solution Helpfull? Yes (4) | No (1)  

surbhi  (12 years ago)

there will be 5! words = 120 words
and the word CHASM will be 31st word when arranged in dictionary order.

Is this solution Helpfull? Yes (3) | No (9)  

bhagyashree puntambekar  (10 years ago)

first, fix A then there will be 24 words starting with A. then 25th word will start with C.Now fix C and A there will be 6 more words. (till now total 30). 31st word will be CHAMS and then 32nd will be CHASM.

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Rohan Bhatnagar  (7 years ago)

The letters when arranged alphabetically are : ACHMS
now we have to find rank of CHASM so
words starting with C are given by C _ _ _ _ i.e 4! =24
now next we have to take CH _ _ _ i.e, 3!= 6
next alphabet according to our alphabets is 'A' given by words starting with CHA _ _
here we have two possible arrangements either CHAMS which will be the 31st word
secondly CHAMS will be having a rank of 32nd.

Hence our answer is 32.

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AHSAN JAMIL SIDDIQUE  (7 years ago)

please explain all the solution clearly.

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uthra murugesan  (8 years ago)

Consider a coding system where C, H, A, S, M = 2, 3, 1, 5, 4 respectively. We want to know the rank of code 23154.

Let's count all of the possible combinations below 23154.

We know that any code starting with 1 is less so we have 4! = 24 possibilities.

We also know that any cod starting with 21 is less so we have 3! or 6 additional possibilities.

For codes starting with 23XXX, only 23145 is less than 23154. so we have a total of 31 codes less than 23154 so the rank of cod 23154 is 32 and the answer, IMO, is (3).
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