Question

a) A teacher and 9 students are to be seated along a bench in the bleachers at a basketball game. In how many ways can this be done if the teacher must be seated in the middle and a difficult student must sit to the teacher’s immediate left?

Answer 1

Given : A teacher and 9 students are to be seated along a bench in the bleachers at a basketball game.

To Find :

In how many ways can this be done if the teacher must be seated in the middle and a difficult student must sit to the teacher’s immediate left?

Solution:

A teacher and 9 students   => Total = 10

Total 10 seats Hence middle seat can be 5 or 6

so teacher can sit in 2ways

and teacher and a students position is fixed  

So remaining 8 students can sit in 8 !  ways

Hence total ways = 2 * 8 !

= 80,640  ways

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