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Mr. and Mrs. Lopez have three children. When they get into their family car, two people sit in the front, and the other three sit in a row in the back. Either Mr. Lopez or Mrs. Lopez must sit in the driver's seat, and their youngest child is not allowed to sit in the other front seat. How many seating arrangements are possible?

 Jun 13, 2021
 #1
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The members are  : Mr.L, Mrs.L, 1st child, 2nd child & 3rd child.

 

  • Either Mr.L or Mrs.L sits in driver's seat

                     No. of possibilities = 2

  • Only 3rd child can't sit in other front seat and either M.L or Mrs.L already sits in drivers' 

                     No. of possibilites in other front seat = (5-2) = 3

  • Of the remaining 3 anyone can seat in any 3 seats in any order 

                     No. of arrangements in the back seats = 3! = 6

 

Thus total seating arrangements \(=2×3×6\)

                                                     \(=36\)

 

 

~ Hope you got it :)  

 Jun 13, 2021
edited by amygdaleon305  Jun 13, 2021

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