Fractal wrote:6 people are in the cinema. paul and rita are not allowed to sit next to each other. also paul and daniela are not allowed to sit next to each other.
number of possibilites how they can sit = ... ?
Paul on either end:
The number of options for Paul = 2.
Since Rita and Daniela cannot sit next to Paul, the number of remaining people who can sit next to Paul = 3.
The number of ways to arrange the 4 remaining people = 4! = 24.
To combine the options above, we multiply:
Number of arrangements = 2*3*24 = 144.
Paul in one of the 4 middle seats:
The number of options for Paul = 4.
Since Rita and Daniela cannot sit next to Paul, the number of remaining people who can sit to the left of Paul = 3.
Since Rita and Daniela cannot sit next to Paul, the number of remaining people who can sit to the right of Paul = 2.
The number of ways to arrange the 3 remaining people = 3! = 6.
To combine the options above, we multiply:
Number of arrangements = 4*3*2*6 = 144.
Total arrangements = 144+144 = 288.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at
[email protected].
Student Review #1
Student Review #2
Student Review #3
