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!

• 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!
• 12 years agoHelpfull: Yes(177) No(3)
• 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
• 12 years agoHelpfull: Yes(37) No(2)
• 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!
• 12 years agoHelpfull: Yes(32) No(9)
• 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)
• 9 years agoHelpfull: Yes(8) No(0)
• 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!
• 12 years agoHelpfull: Yes(4) No(41)
• 20!-(19!2!)=18*19!
  
• 12 years agoHelpfull: Yes(3) No(2)
• 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)
• 5 years agoHelpfull: Yes(0) No(0)