Latest Infosys Aptitude Question SOLUTION: In how many ways can the letters in mmmnnnppqq can be arranged with two n's together?

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In how many ways can the letters in mmmnnnppqq can be arranged with two n's together?

Asked In Infosys krishnaveni (8 years ago)

Unsolved Read Solution (29)

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Read Solution (29) :

siddhartha ganguly  (8 years ago)

MMMN(NN)PPQQ so taking two N's together we can get =9!/(3!*2!*2!) arrangements
bow this NN can be arranged in =2!/2!=1 ways
so total arrangements=9!/(3!*2!*2!)=15120 ways

Is this solution Helpfull? Yes (53) | No (12)  

Aditi Srivastava  (8 years ago)

Ans: 7560
since 2 n's are to be considered as one entity
now, we have 9 letters out of which we have to select 9 and arrange them
selecting and arranging 9= 9C9 x 9! / 3! x 2! x 2! x 2!= 7560

Is this solution Helpfull? Yes (23) | No (15)  

krishnaveni  (8 years ago)

count where two n's are not together=total arrangement -where the n's are together.
total arrangement=10!/(3!*3!*2!*2!)-((8C3*3!/3!)*(7!/3!*2!*2!))=13440 ways

Is this solution Helpfull? Yes (9) | No (2)  

Rahul  (8 years ago)

9!/(3!*2!*2!)

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

KUNA VENKATA LAKSHMI NARAYANA RAO  (8 years ago)

i am pongadam. my solution is (9!/3!2!2!-8!/3!2!2!)

Is this solution Helpfull? Yes (5) | No (1)  

Vivek Badde  (8 years ago)

only Krishnaveni solution is correct:10!/(3!*3!*2!*2!)-((8C3*3!/3!)*(7!/3!*2!*2!))=13440 ways

Is this solution Helpfull? Yes (3) | No   

Samridhi  (8 years ago)

since 2 n's are together, total number of groups available becomes 9 which can be arranged in 9! ways.
now since, there r 3 m, 2 p and 2 q .. so it would become 9!/(3!*2!*2!).. further 2 n can be arrange themselves in 2! ways .. and being repetative total arrangemnt possible for the two grouped n is 2!/2!..
so the answer eventually turn out to be 9!/(3!*2!*2!)

Is this solution Helpfull? Yes (3) | No   

Savi Jindal  (7 years ago)

total number of ways when two n's are together = 9!/(3!*2!*2!)
Now subtracting the cases when three n's are together(because they are considred twice eg.= mmmn(nn)ppqq and mmm(nn)nppqq ) = 8!/(3!*2!*2!)
therefore, total arrangements = 9!/(3!*2!*2!)- 8!/(3!*2!*2!) = 13440 ways

Is this solution Helpfull? Yes (3) | No   

Ramesh Panchadhi  (8 years ago)

9!/(3!*2!*2!)

Is this solution Helpfull? Yes (2) | No (5)  

Nandhini  (8 years ago)

in 7560 ways since in 3 N's N's is considered to b single soooooo it will bw like 9!/3!2!2!

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

Pragadeeswara Prabhu  (8 years ago)

Arranging with 2 n’s together:
Select 2 n’s out of three = 3C2 = 3
The selected 2 n’s are considered as one.
There will be 9 elements after combining.
Number of arrangements,
= [9!/(3! x 2! x 2!)] x (2!/2!) x 3
= 11340
In the above arrangements, some them will have 3 n’s together. We have to eliminate them.
Number of arrangements in which 3 n’s are together, = [8!/(3! x 2! x 2!)](3!3!)
= 420
Number of arrangements in which 2 n’s are together,
= 11340 – 420 = 10920

Is this solution Helpfull? Yes (2) | No   

abhinav bahl  (8 years ago)

total number of letters=10
ways in which 10 letters can be arranged=10 !
ways in which 9 letters can be arranged(since 2 n's allways occur together)-9!(arranging 9 letters)*2(since two n's can be arranged in 2! ways)

Is this solution Helpfull? Yes (1) | No   

meghana  (8 years ago)

taking 2 N's are one unit
9!/3!2!2!1!

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

ARGHYA GHOSH  (8 years ago)

total no.of ways in which the letters can be arranged=10!/(3!*3!*2!*2!)=25200
taking 2 N's as 1 unit,we have to arrange MMM(NN)NPPQQ=9 letters,
this can be done in=9!/(3!*2!*2!)=15120 ways.
out of these 15120 ways,the 2 N's can be arranged between themselves in 2!/2!=1 way.
thus the total no.of ways=25200-(15120*1)=10080 ways.

Is this solution Helpfull? Yes (1) | No   

harsha vardhan  (8 years ago)

9!*2!
9! ways for all alphabets and 2! ways for 2 ns as a unit

Is this solution Helpfull? Yes | No (2)  

Sanjay Kumar  (8 years ago)

9!/(3!*3!*2!*2!)

Is this solution Helpfull? Yes | No (3)  

Vipin Prasad Saxena  (8 years ago)

9!*2!=725760

Is this solution Helpfull? Yes | No   

Vignesh  (8 years ago)

mmm(nn)nppqq = 9!*2! = 725760

Is this solution Helpfull? Yes | No   

Saurav Kumar  (8 years ago)

Two n's together=No restriction-Three n's together
so ans=10!/(3!*3!*2!*2!)-8!(3!*2!*2!)

Is this solution Helpfull? Yes | No (2)  

Raghvendra Sharma  (8 years ago)

if we take 2n together then...
mmmn(nn)ppqq=9
so 9!/(3!*2!*2!*2!)=7560
so 7560 is the ans.

Is this solution Helpfull? Yes | No   

RISHABH GUPTA  (8 years ago)

(8! * 3C2)/(3! * 2! * 2!) = 5040

Is this solution Helpfull? Yes | No   

MANOJ  (8 years ago)

mmmnnnppqq. therefore mmmnppqq(nn).There are 9 elements in which m has 3 repeatation p has 2 q has 2 .. so 9!/(3*2*2) =362880/12= 30240. since n can be arranged in 2! ways. 30240*2! = 60480

Is this solution Helpfull? Yes | No   

Charmy  (7 years ago)

taking NN together we get = 9!/(3!*2!*2!)
and NN can be arranged in = 2!
thus total arrangements = (9!/3!*2!*2!)*2! = 30240

Is this solution Helpfull? Yes | No   

karthik shaoo  (7 years ago)

9!/(3!*3!*2!*2!)

Is this solution Helpfull? Yes | No   

Ashish Pradhan  (6 years ago)

(NN)MMMNPPQQ (Note that NN is treated as one letter)
Taking two N's together we can get (9!*2!)/(3!*2!*2!) arrangements ..
(9!*2!) => NN can be arranged in 2! ways & MMMNPPQQ+(NN) = 9 letters
(3!*2!*2!) => M is repeated 3 times, P is repeated 2 times & Q is repeated 2 times

Is this solution Helpfull? Yes | No   

Akash Jain  (6 years ago)

13440 is correct

Is this solution Helpfull? Yes | No   

manoj  (5 years ago)

ans: 7!/2! * 8!/3! 2! 2!

two n's together in 7 positions -----> _m_m_m_n_p_p_q_q_ (two positions excluded)
but two positions excluded because mmm(nn)nppqq and mmmn(nn)ppqq (three n's are together)
and again two n's internally can be arranged in 2! ways So, 7!/2! ways two n's together and remaining letters can be arranged in 8!/3! 2! 2!

so finally, 7!/2! * 8!/3!2!2!

Is this solution Helpfull? Yes | No   

Subhradeep Ghosh  (5 years ago)

9!/3!*2!*2!*2!=7560

Is this solution Helpfull? Yes | No   

HARISH S  (5 years ago)

Ans: 13440
Count where two n's are together = Total arrangements - where the n's are not together

Total arrangements = 10!/(3!*3!*2!*2!) = 25200

Now let us find the count where no two n's are together. For this n's can occupy the 8 positions which are represented by blanks.
_ m _ m _ m _ p _ p _ q _ q _
Out of these 8 positions, 3 positions can be chosen in 8C3 ways. In these 3 positions the three n's can be arranged in 8C3 * 3!/3! = 8C3 = 56 ways.
The m,p,q can be arranged among themselves in 7!/(3!*2!*2!) = 210 distinct ways.
So overall ways of arranging = 56*210 = 11760 ways.

Hence number of ways in which two n's are together = 25200 - 11760 = 13440 ways

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