Question

In how many ways can aling rosa arrange 6 potted plants in a row?

Answer 1

6 potted plants can be arranged 720 different ways.

Answer 2

Consider 6 potted plants that you are going to arrange in a row. You can choose first plant in 6 ways (one plant from 6 given), then 5 plants left to be arranged. The second plant can be chosen in 5 ways (one plant from remaining 5) and after you arrange the second plant, only 4 plants left. The third plant you can choose in 4 ways (one plant from remaining 4) and after this procedure only 3 plants left. The fourth plant you can choose in 3 ways (one plant from remaining 3) and only 2 plants left. The fifth plant you can choose in two ways and the last one is determined by the 5 previous.

Then the number of ways to arrange 6 potted plants in a row is

$6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1=6!=720\ ways.$

Answer: 720 ways