Question

The governor is making a visit to your school and you need to assign seating for 14 students. Unfortunately there are only six seats in the front row. In how many different ways can you select and arrange the six lucky students?

a.

2,162,160 different ways


b.

1 different way


c.

84 different ways


d.

20,160 different ways

Answer 1

Since the problem is concerned of the arrangement in the first row, this can be solved through permutation. Above is a permutation of 14 taken 6 which can be easily solved through the calculator or through the equation,
14P6 = (14!)/(14-6)!
= 2162160
Thus, the answer is letter A.

Answer 2

This is a permutation problem with 14 elements that can only be taken 6 at a time. In permutation notation,
14P6
which in factorial form is
14! / (14 - 6)!
which is equal to
= 2162160

The answer is
2,162,160 different ways