SOLUTION: find the permutation of number of ways in which 5 first year student and 5 second year student can be seated on a bench in a examination hall so that no two students of the same cl

Algebra ->  Permutations -> SOLUTION: find the permutation of number of ways in which 5 first year student and 5 second year student can be seated on a bench in a examination hall so that no two students of the same cl      Log On


   

Question 994009: find the permutation of number of ways in which 5 first year student and 5 second year student can be seated on a bench in a examination hall so that no two students of the same class are next to each other ?
Answer by KMST(5328) About Me  (Show Source):
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You will have to sit them alternating one student from each class.
The first choice is:
should the student sitting to the left of all other students be a first year student or second year student?
You have 2 choices.
For each of those choices, you have more choices that are independent of each other.
You have to decide:
in what order to sit the first year students, and
in what order to sit the second year students.
There are 5%21=5%2A4%2A3%2A2%2A1=red%28120%29 possible orders to sit the first year students.
There are 5%21=5%2A4%2A3%2A2%2A1=green%28120%29 possible orders to sit the first year students.
All in all, there are 2%2Ared%28120%29%2Agreen%28120%29=highlight%2828800%29 ways in which 5 first year student and 5 second year student can be seated on a bench in a examination hall so that no two students of the same class are next to each other.