Are These Answers Correct?

Roses Are Red said:

1. In how many ways can 10 instructors be assigned to eight sections of a course in mathematics?

My answer: 10 P 8 = (10!)/(10-8)! = 10!/2! = 3628800/2 = 1814400

2. In how many different ways can the top ten new indie bands be ranked on a top ten list? The top hit song for each of the ten bands will compete to receive monetary awards of $1000, $500, $250 and $100, respectively. In how many ways can the awards be given out?

My answer:
10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 3,628,800
10 x 9 x 8 x 7 = 5,040 ways

Click to expand...

Roses Are Red said:

1. In how many ways can 10 instructors be assigned to eight sections of a course in mathematics?

My answer: 10 P 8 = (10!)/(10-8)! = 10!/2! = 3628800/2 = 1814400

2. In how many different ways can the top ten new indie bands be ranked on a top ten list?

The top hit song for each of the ten bands will compete to receive monetary awards of $1000, $500, $250 and $100, respectively. In how many ways can the awards be given out?

My answer:
10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 3,628,800
10 x 9 x 8 x 7 = 5,040 ways

Click to expand...