Latest TCS Aptitude Question SOLUTION: Mr and Mrs Smith have invited 9 of their friends and their spouses for a party at the Waikiki Beach resort. They stand for a group photograph. If Mr Smith never stands next to M

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Mr and Mrs Smith have invited 9 of their friends and their spouses for a party at the Waikiki Beach resort. They stand for a group photograph. If Mr Smith never stands next to Mrs Smith (as he says they are always together otherwise). How many ways the group can be arranged in a row for the photograph?
A. 20!
B. 19! + 18!
C. 18 x 19!
D. 2 x 19!

Asked In TCS kanika (11 years ago)

Unsolved Read Solution (7)

Is this Puzzle helpful?   (58)   (22) Submit Your Solution Permutation and Combination

Read Solution (7) :

lala  (11 years ago)

C) 18*19!


total 20 persons are there..
we can arrange them in 20!ways
consider Mr.& Mrs.smith take them as a unit so 18+1=19
19!2! cases are there when they are together which is not allowed here.
so possible arrangements = 20!-(19!2!)= 19!(20-2) = 18*19!

Is this solution Helpfull? Yes (177) | No (3)  

Mukta Yadav  (11 years ago)

since Mr.& Mrs. SMITH can never stand together..so they can sit anywhere between their 18 friends. so freinds can be arranged in 18! places. now between freinds 19 spaces are left.
Mr. n mrs. smith can occupy any 2 places..i.e..19C2.AND can be arranged in 2 ways.
therefore..ans is 19c2*2*18!= (19!/(2*17!)*2!*18!=18*17!*19!/17! = 18* 19!
hence..ans =c

Is this solution Helpfull? Yes (37) | No (2)  

Sougata Sarkar  (11 years ago)

option c
if we consider that mr & mrs smith is a group. then the probability is (18+1)!=19!
but Mr & Mrs smith are arranged any which is 18.
so the probability is 18*19!

Is this solution Helpfull? Yes (32) | No (9)  

prem sukh  (8 years ago)

there are 9 friends and there spouse, so total friends=18
so total number of people in party=18+2=20(including mr and mrs smith)
total number of possible arrangement=20!
total number of arrangement in which mr and mrs are together is =19!*2!
so total number of arrangement in which mr and mrs are not together =20!-!(19!*2!)
=(20*19!)-(19!*2!)
=19!(20-2)
=19!*18(ans)

Is this solution Helpfull? Yes (8) | No   

shyam salona  (11 years ago)

total peoples=20
total no of permutation=20!
but mr n ms smith never stand together
so
permutations when they are together can be find by considering them as a unit so permutation=19!
so required solution=20!-19!=19!(20-1)= 19*19!

Is this solution Helpfull? Yes (4) | No (41)  

Rahul Pandey  (11 years ago)

20!-(19!2!)=18*19!

Is this solution Helpfull? Yes (3) | No (2)  

Tridib Samanta  (4 years ago)

Mr. and Mrs. Smith invited 9 of their friends and their spouses.
∴, total 20 persons are present there. 
They can be arranged in 20! ways.
Now, if we consider that Mr. Smith stands with Mrs. Smith always then we can consider them as 1 person. Then remining (20-1)=19 persons can be arranged in 19! ways and the position of Mr. and Mrs. Smith can be arranged in 2! ways.
∴, the required number of arrangement is:
20!-19!×2!
=20×19!-19!×2×1
=19!(20-2)
=18×19! (Ans)

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