4 people are sitting in a 4 seat row watching a football game.
4 people are sitting in a 4 seat row watching a football game. At halftime they all get up. When they return, they each randomly sit down on one of the 5 chairs. What is the likelihood that none of the 4 end up sitting in the same chair that they sat in during the first half?
Answer/Solution
3/4
Steps/Work
Originally seated A B C D
now when after they get up and when they sit back again .
1st- A has option to sit on 3 seats ( apart from his previous seat . thus he now sits on B's seat.)
2nd- Similarly B has option to sit on 3 seats ( because A has already occupied B's previous seat, thus B sits on a's seat.)
3rd- Now C has only 1 option to sit on D's seat . and similarly D also has one option to sit on C's seat.)
hence total favourable outcomes 3*3*2*1*1=18
and total possible outcomes =4!=24
probability of the favourable outcome= 3/4. B
now when after they get up and when they sit back again .
1st- A has option to sit on 3 seats ( apart from his previous seat . thus he now sits on B's seat.)
2nd- Similarly B has option to sit on 3 seats ( because A has already occupied B's previous seat, thus B sits on a's seat.)
3rd- Now C has only 1 option to sit on D's seat . and similarly D also has one option to sit on C's seat.)
hence total favourable outcomes 3*3*2*1*1=18
and total possible outcomes =4!=24
probability of the favourable outcome= 3/4. B