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.

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