Letters arrangement (1 Viewer)

[juantheron]

In how many ways 4 letters can be posted in 5 letter boxes.


ans: = each of the 4 letters can be posted in any one of Letter boxes in 5 ways .

So Using Principle of Multiplication

Total no. of ways is = 5*5*5*5 = 5^4

But I have a confusion

Can we not post

all letters in one Letter Box or all letters in (II) letters box or all letters in (III) letters box or all letters in (IV) letters box or all letters in (V) letters box

Why this is Not True

Can anyone explain me briefly .

Thanks

 

[Carrotsticks]

Your logic there IS true, but it only counts a very small portion of all possible events.

The first letter can go into any 5 boxes, so we have 5 ways.

The second letter can go into any 5 boxes, so we have 5 ways.

...

The fifth letter can go into any 5 boxes, so we have 5 ways.

So therefore we have 5x5x5x5 = 5^4 ways.

And this INCLUDES the possible case where all letters are in the same box.

 

[juantheron]

Thanks Moderator