Mr and Mrs smith have invited 9 of their friends and their spouses for a party at the waikki beach report.they stand for a group hotograph.if Mr smith never stand next to the Mrs smith(as he says there are always together otherwise),how many
ways the group csn be arranged in a row for the photograph.
A.2x19!
B.20!
C.18x19!
D.19!+18!

• ans option c)18*19!
  
  Lets first deduce the no of ways where the Mr and Mrs smith are together and then subtract this from the total possible combination to get the reqd. ways.
  
  9 friends with their spouses makes it 18 people(with no restrictions) and smith couple is treated as one unit.
  =>then total no of ways (18+1)*2!(two ways of arranging the smith couple ).
  =>2*19! are the ways where Mr and Mrs smith will be together.
  =>Subtracting it from the total possibilities of 20! , we get
  =>20!-2*19!
  =>20*19!-2*19!
  =>19!(20-2)
  =>18*19!
  
• 10 years agoHelpfull: Yes(39) No(0)
• there are 10 couples.. (including mr n mrs smith)
  no. of ways they all can stand in a row = 20!
  consider mr and mrs smith as 1 person.. therefore now 19 person are there..
  so no. of ways these 19 people can stand is = 19!* 2 (2 is multiplied coz mr n mrs can interchnge there place wid each other)
  therefore.. no. of ways in wch mr and mrs nevr stand wid each other = 20!-(19!*2) = 18*19!
• 10 years agoHelpfull: Yes(17) No(0)
• firstly 9 couples can be arranged in 18! ways.
  there are 19 places in between them so they can select places in 19c2*2! ways multiplied with 2! because they can be interchanged with each other.
  finally they can be stand in 18!*19c2*2!=18!*19*18=18*19!
• 10 years agoHelpfull: Yes(3) No(0)
• as he no. of friends and their spouses make it 18 and if mrs. n mr. smith ar 1 unit then total 19 which makes arrangement 2*19! thus subtracting fro total no. of arrangements we get 20!- 2*19! = 18*19!
• 10 years agoHelpfull: Yes(0) No(0)
• there are 20 persons so no. of arrangements=20!
  then if we take Mr. and Mrs smith as a group then no. of arrangements=19!*2!
  now 20!-19!*2=19!(20-2)=18*19!
• 10 years agoHelpfull: Yes(0) No(0)