Discrete Mathematics Permutations Question 19 a How many way

Discrete Mathematics Permutations Question:

19. a) How many ways may ten students be arranged in a line so that student 6 always comes before student 2?

b) Generalize the previous problem to n students, where one particular student must come before another particular student.

Solution

Q19)

There are 10 students, you can club the two students as one i.e. make a pair of 2 and student 6

Hence number of permutations will be 9!

But that duplet can be placed in two ways i.e. 2!

Hence number of ways will be 9! * 2! ways

b)

There are n students, you can club the two students as one i.e. make a pair of 2 and student 6

Hence number of permutations will be (n-1)!

But that duplet can be placed in two ways i.e. 2!

Hence number of ways will be (n-1)! * 2! ways