Mr. and Mrs.Smith invited 9 of their friends and their spouses at the party.they stand for a group photograph.If Mr.Smith never stand next to Mrs.Smith.In how many ways group can be arranged in a row for the photograph?
a)20!
b)19!+18!
c)18*19!
d)2*19!

• in the above problem mr.smith and mrs. smith can not come stand together....
  so first we consider the ways by which we can arrange the row in which mr. and mrs. smith always standnext to each other.
  
  9 frnds and there spouses so total number of person except mr. and mrs. smith is
  18 so we can arrange these person in !18 ways and if we consider mr. and mrs. smith a one person then total numbeer of ways in which mr. and mrs. smith always stand next to each other=!19*!2
  
  !2 implies that we can arrange mr. & mrs. smith in !2 types in which they stand next to each other.
  now we consider total number of ways by which we can arrange the row without ny condition is !20 because there are 20 person in the party inculding mr. & mrs. smith.
  so total number of ways=!20
  now according to question total number of ways by which to arrange a row in which mr. & mrs. smith can not stand next to each other
  =!20-!19*!2
  =!19(20-2)
  =!19*18
  =18*!19
  so option c is correct ask queries if anyone didnt get the answer...
  thanku
  
• 12 years agoHelpfull: Yes(46) No(1)
• ans: c......since including one from Mr. or Mrs. smith they can be arranged in 19! and remaining one should be stand in 18 ways...therefore 18 x 19!
• 12 years agoHelpfull: Yes(7) No(0)
• total 20 persons are there..
  we can arrange them in 20!ways
  let mr.&Ms.smith take them as a unit so 18+1=19
  19!2! they should not be together so 20!-(19!2!)
  ans: 18*19!
  
  
• 12 years agoHelpfull: Yes(4) No(0)
• total no of people who were present in the photograph=20
  So total no of ways of arranging 20 people in a photograph =20!
  Since we have to find total no of arrangements in which Mr. and Mrs. Smith are not together
  we will find no of ways in which Mr. and Mrs. smith are together and subtract it frm the total no of arrangements ..
  total no of ways in which Mr. and Mrs .Smith are together in a photograph =19!x2!
  
  so total no of ways in which Mr and Mrs smith are not together is equal to
  20!-(19!x2!)=18*19!
• 12 years agoHelpfull: Yes(2) No(1)
• ANS: b) 19!+18!
  solution:
  9c2=(9*8)/(2*1)=36!=19!+18!
  
• 12 years agoHelpfull: Yes(0) No(5)
• 19!-20!*2!=18*19!
• 12 years agoHelpfull: Yes(0) No(0)