### Arranging things again

#### by rangr

I may have been a little confusing last time. This time, I think, I will be clear,

You can have 5 objects and two places. Two ways of thinking about the same thing is,

FIRST

1)place any of 5 objects in place 1.

2)place any of remaining 4 objects in place 2.

5*4 is 5P2

Similarly,

SECOND

1)place “place 1” on any of the 5 objects.

2)place “place 2” on any of the remaining 4 objects.

5*4 is 5P2.

5! is nothing but

1)place “place 1” on any of the 5 objects.

2)place “place 2” on any of the remaining 4 objects.

3)place “place 3” on any of the remaining 3 objects.

4)place “place 4” on any of the remaining 2 objects.

5)place “place 5” on any of the remaining 1 objects.

3! is nothing but

3)place “place 3” on any of the 3 objects.

4)place “place 4” on any of the remaining 2 objects.

5)place “place 5” on any of the remaining 1 objects.

Now 5P2 is nothing but

First 2 steps of the above procedure. i.e. deleting 3! from 5!. Hence the formula 5P2 is 5!/3!.

Hope this is clear.

Note: Both ways of thinking either placing objects on places or places on objects is equivalent.