Latest TCS Aptitude Question SOLUTION: "LEADING" arrange it in such a way that atleast two vowels always together...??

• Placement Papers
• /
• TCS
• /
• Numerical Ability
• /
• Permutation and Combination

TCS Question Papers: TCS Interview Experience(90) TCS Company Profile

(#M40024623) TCS Numerical Ability question Keep an EYE

"LEADING" arrange it in such a way that atleast two vowels always together...??

Asked In TCS Akhilesh Agrawal (10 years ago)

Unsolved Read Solution (37)

Is this Puzzle helpful?   (25)   (7) Submit Your Solution Permutation and Combination

Read Solution (37) :

aakash  (10 years ago)

3c2*(6!*2!) + 3c3*(5!*3!)

Is this solution Helpfull? Yes (55) | No (5)  

Prakhar Gupta  (10 years ago)

There are 2 possiblities i.e.
1) Either all the three vowels will come together
2) Or 2 vowels will comes together

for 1st condition LONG "EAI" = LONG with "EAI" can arrange in !5 ways and then "EAI" can arrange in !3 ways therefore !5 * !3 = 120*6=720

Now same for the second 1 LONGI "EA" can arrange in !6 possible ways but "EA" only can arrange in !2 ways and therefore !6*!2= 720* 2= 1440

Now the total no. of ways of arranging these 2 = 1440+720= "2160"

Ans = 2160

Is this solution Helpfull? Yes (47) | No (31)  

Ravi Kant Sharma  (10 years ago)

in LEADING there are 3 vowels.
if 2 vowels fix then arrangement will be 6!*2!
if 3 vowels fix then arrangement will be 5!*3!
now total ways will be (6!*2!)+(5!*3!)=2160 ans

Is this solution Helpfull? Yes (28) | No (5)  

Shreyansh Jain  (10 years ago)

(6!*2!*3)+(5!*3!)=5040

Is this solution Helpfull? Yes (25) | No (2)  

MOUNIKA REDDY  (10 years ago)

(total)- (no two vowels come together)
total=7!
no two vowels come together={_L_D_N_G_)=4!*(5C3*3!)
7!-(4!*5P3)=3600

Is this solution Helpfull? Yes (17) | No (8)  

Anand R. Patel  (9 years ago)

There are two possibilities :-
1) Either all the three vowels will come together
2) 2 vowels will come together

Case 1 :- All three vowels come together
If three vowels E,A & I come together they can taken as one group EAI
now we have only 5 words to arrange i.e. L,D,N,G,EAI
They can be arranged in 5!*3!=720 ways

Case 2 :- Only two vowels come together

In this case we have to select which two vowels come together in order to make them in one group

this groups can be :- EA or AI or EI total 3 groups(3C2=3 groups)
So, total ways for this case=3*6!*2!=4320.

So.final ans is=4320+720=5040

Is this solution Helpfull? Yes (16) | No (2)  

Akhilesh Agrawal  (10 years ago)

6!2!+5!3!...????

Is this solution Helpfull? Yes (10) | No (5)  

Neha Sharma  (10 years ago)

The word 'LEADING' has 7 different letters.

When the vowels EAI are always together, they can be supposed to form one letter.

Then, we have to arrange the letters LNDG (EAI).

Now, 5 (4 + 1 = 5) letters can be arranged in 5! = 120 ways.

The vowels (EAI) can be arranged among themselves in 3! = 6 ways.

Required number of ways = (120 x 6) = 720.

Is this solution Helpfull? Yes (9) | No (17)  

chalamalasetti  (10 years ago)

but prahar gupta in the case of two vowels come together here we can arrange the vowels in 3 ways LDNG+(A or E or I =LDNGA or LDNGE or LDNGI) and the reamining two vowel letters arrange it in two ways so 2! hence total 6!*2!*3+5!*3!

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

aayush kumar  (10 years ago)

here it is given that "at least" 2 vowels alwys toghtr so it can b 2 or three !! so if we will sbtract (total no of arrngmnt-no vowels togthr )we will get the answr . total no of arrngmnt=7!=5040 .
and no of ways to arrnge s.t no vowels togethr=4!*5p3=1440.
so ans=5040-1440= 3600

Is this solution Helpfull? Yes (6) | No (2)  

Bailore Pradyumna Acharya  (10 years ago)

3600 is the right answer...

Is this solution Helpfull? Yes (3) | No (1)  

Prasanna krishna  (10 years ago)

7!-3!*5! = 720

Is this solution Helpfull? Yes (2) | No (6)  

amit   (10 years ago)

3c2*!2*!6+3c3*!3*!5

Is this solution Helpfull? Yes (2) | No (1)  

Akhilesh Agrawal  (10 years ago)

LE'AI'DNG and L'EAI'DNG is the same permutation , when you consider two vowels in the first case and there vowels in the second case.

So, 'three vowels together' appears in a 'two vowel together' word when the other vowel comes near the pair of vowels

Is this solution Helpfull? Yes (1) | No   

Ankur Raghuwanshi  (10 years ago)

36oo........7!-4!(5c3*3!)

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

Neeraj Kumar  (10 years ago)

LEADING
TAKE ANY TWO VOWELS
(LDING)*(EA)
6!=720
NOW
2! FOR TWO VOWELS
2!=2
TOTAL=720*2=1440

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

Guru Pranav  (10 years ago)

Answer is 2160 !!!

Is this solution Helpfull? Yes (1) | No   

Antra Addy  (10 years ago)

DEALING
Two vowels E and A are together.

Is this solution Helpfull? Yes | No (8)  

Akhilesh Agrawal  (10 years ago)

we have to find no of arrangement

Is this solution Helpfull? Yes | No (2)  

sreetej  (10 years ago)

atleast 2 and atleast 3 are two chances as there are 3 vowels
so answer id (3p2 * 5!) + (3! *4!) = 864

Is this solution Helpfull? Yes | No (2)  

aayush kumar  (10 years ago)

ans :- 2880

Is this solution Helpfull? Yes | No (2)  

Himanshu jain  (10 years ago)

720
5!=120
then here are 3 vowels then arrange atleast two vowels always together so only 3 case are possible IE , EA, AI so 3!=6
so total is 120*6=720

Is this solution Helpfull? Yes | No (2)  

AKASH SINGH  (10 years ago)

Number of ways= 3P2*6!+3P3*5!

Is this solution Helpfull? Yes | No (1)  

sabbineni sri lasya  (10 years ago)

2160 is d ans

Is this solution Helpfull? Yes | No (2)  

Amsaveni Natarajan  (10 years ago)

=(6!*2!)+(5!*3!)
=2160

Is this solution Helpfull? Yes | No (3)  

Vaibhav Tyagi  (10 years ago)

ans is 5!*3!=720

Is this solution Helpfull? Yes | No (2)  

Vivek Prajapati  (10 years ago)

2160
as 7!-(4!*5!)
{total ways- ways having no two vowels together}

Is this solution Helpfull? Yes | No   

Sumit Chopra  (10 years ago)

since atleast 2 vowels should be together i.e either EI/AI/EA.
Now for the first case EI---LADGN(EI)---5!2!5! (6! for total, then 2! for EI and 5! for LADGN)....similarly for AI and EA... so 2*5!2!5!

then in case where 3 vowels are to be selected----LDNG(AEI)---5!4!3! (5! for total , 4! for LDNG and again 3! for AEI)..
hence total ways (2*(5!2!5!))+ 5!4!3!

Is this solution Helpfull? Yes | No   

basanagouda  (10 years ago)

i think it is=(5!*2!)+(6!*2!*3c2) bcz while taking 2 vowels at a time those two can be selected in 3 ways na....

Is this solution Helpfull? Yes | No   

PRATEEK  (10 years ago)

(AEI)LDNG,,,Take all vowels as one now total cases 5! and vowels position can also interchange with each other like 3!so(5!*3!)=720

Is this solution Helpfull? Yes | No   

Anindya Mallick  (8 years ago)

6!*2! smple..consider only 2 vowels have to b together.

Is this solution Helpfull? Yes | No   

JIT BHATTACHARJEE  (8 years ago)

5!*3!+6!*2!=2160

Is this solution Helpfull? Yes | No (1)  

shivaram akumalla  (8 years ago)

when i solved im getting 5040 ie.(5!*3!+(6!*3c2*2!)) . but its showing answer is 2160. which one is correct guys ?

Is this solution Helpfull? Yes | No   

Sanket  (8 years ago)

(lead)(eai)=5!*3!=720
leada (ei)=6!*2=1440
leadi (ea)=6!*2=1440
leade (ai)=6!*2/2=720 as e is repeating in main so answer is 4320.

Is this solution Helpfull? Yes | No   

Vishal Kumar  (8 years ago)

There are 2 possiblities i.e.
1) Either all the three vowels will come together
2) Or 2 vowels will comes together

for 1st condition LONG "EAI" = LONG with "EAI" can arrange in !5 ways and then "EAI" can arrange in !3 ways therefore !5 * !3 = 120*6=720

Now same for the second 1 LONGI "EA" can arrange in !6 possible ways but "EA" only can arrange in !2 ways and therefore !6*!2= 720* 2= 1440 same for "EI" ans "AI"

Now the total no. of ways of arranging these 2 = 1440*3+720= "5040"

Ans = 2160

Is this solution Helpfull? Yes | No   

prakhar  (8 years ago)

Total possible arrangement = 7! = 5040
total=7!
when no 2 vowel comes together : {_L_D_N_G_)
here 3 vowels can be placed in 5 positions and the vacant space will be removed so : 5p3 * 4! = 60*24 = 1440.
So required arrangements : (5040 - 1440) = 3600

Is this solution Helpfull? Yes | No (1)  

raghav  (4 years ago)

2160
5!*3! +6!*2! =2160

Is this solution Helpfull? Yes | No   

Please Login to Read Solution.