Latest TCS Aptitude Question SOLUTION: The letters in the word ADOPTS are permuted in all possible ways and arranged in alphabetical order then find the word at position 42 in the permuted alphabetical order? (a) AOTDSP

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(#M40024308) TCS Logical Reasoning question Permutation Keep an EYE

The letters in the word ADOPTS are permuted in all possible ways and arranged in alphabetical order then find the word at position 42 in the permuted alphabetical order?
(a) AOTDSP
(b) AOTPDS
(c) AOTDPS
(d) AOSTPD

Asked In TCS Muthu Yogalakshmi.N (10 years ago)

Unsolved Read Solution (8)

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Read Solution (8) :

Karthika  (10 years ago)

In alphabetical order : A D O P S T
A D _ _ _ _ : empty places can be filled in 4!=24
A O D _ _ _ : 3!= 6
A O P _ _ _ : 3!=6
till this 36 words r obtained,we need the 42nd word. SO
then
37: A O S D P T
38: A O S D T P
39: A O S P D T
40: A O S P T D
41: A O S T D P
42: A O S T P D --> 42nd word

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Karthika  (10 years ago)

Take example "DEAR".find 8th word
write the letters in "DEAR" in alphabetical order.
A D E R
STart with A _ _ _ (in dictionary every word starts with A)..here the empty places can b filled in 3! ways=6 (i.e ADER,ADRE,AEDR,AERD,ARDE,ARED)- 6 words
next take D _ _ _ =3! =6 words. but v need the 8th word. hence we reduce the empty spaces i.e
we know D A _ _ =2!=2 words (DAER, DARE )
hence DARE is the 8th word.

@Devika and Ipsita : hope yu understud...

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Muthu Yogalakshmi.N  (10 years ago)

Answer Explanation:

(ADO)(PST)-Alphabetial order
(AOD)(PST)-Can be arrange in 3! ways=6
(AOP)(DST)-Can be arrange in 3! ways=6
(AOS)(DPT)-Can be arrange in 3! ways=6
(AOT)(DPS)-Can be arrange in 3! ways=6
(AOT)(PSD)-Can be arrange in 3! ways=6
(AOP)(TSD)-Can be arrange in 3! ways=6
(AOS)(TPD)-Can be arrange in 3! ways=6
6+6+6+6+6+6+6=42
So,"AOSTPD" Would be the 42th word.

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lucky  (10 years ago)

arrange the words alphabetically A,D,O,P,T,S
start with A _ _ _ _ _ ways 5!=120 it is more than required
so put D at second pos AD _ _ _ _ ways 4!=24 now replace D with O
AO _ _ _ _ 4!=24 ways total 24+24=48 more than required so put thirs letter
AOD _ _ _ 3!=6 so ways till now 24+6=30 doing the same we will reach AOSTPD at 42nd postion

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Sujithra  (9 years ago)

to devika, muthu yogalakshmi and ipsita saha..
first take the given letters of a word in alphabetical order..
adopst...
if a is the first word then the remaining 5 letters can be arranged in 5! ways (i.e) 120 ways but it is more than 42
so take the next alphabet in order next to a
now consider ad then remaining 4 letters can be arranged as 4!=24 which is lesser than 42 so take the next possibility as ao now we get another 24 ways so totally 48 ways from ad and ao... 42 lies in ao so take the next letter as aod then the remaining will be arranged as 3!=6 ways but 24 ways +6 ways is 30 so choose another letter as aop which gives another 6 ways so totally 36 words so the next will aos ehich gives another 6 ways which is equal to 42.. we need to find the 6th way in the aos combination.. choose the next letter aosd will be = 2 ways and we need the 6th way and so choose the next lettet in alpha order aosp which gives upto 40 th word and so select aost which gives the 41st and 42nd word now we need to find the 2nd word in aost combination whch is aostpd

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Devika.R  (10 years ago)

hi karthika,i cant understand these types of ques til now......can u explain the logic behind it

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Muthu Yogalakshmi.N  (10 years ago)

Ans:(d) AOSTPD

Pls anybody explain the answer.

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ipsita saha  (10 years ago)

pls exlpn the logic behind these type of problms

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