<PRE><B>Question 601074</B>
There are 12 places to pick a place for the 1st egg,
For each of those 12 places, there remain 11 places to put the 2nd egg.
That 12ｷ11 ways to place the first two 3ggs.
&lt;pre&gt;

Factoriala ARE permutations.

The best way is to think it out:

There are 12 ways to place egg #1 in the carton.

For each of those 12 ways to place the 1st egg, there
remain 11 places in the carton to place egg #2.
That&#39;s 12ｷ11 ways to place the first 2 eggs in the
carton.

For each of those 12ｷ11 ways to place the 1st 2 eggs,
there remain 10 places in the carton to place egg #3.
That&#39;s 12ｷ11ｷ10 ways to place the first 3 eggs in the
carton.

For each of those 12ｷ11ｷ10 ways to place the 1st 3 eggs,
there remain 9 places in the carton to place egg #4.
That&#39;s 12ｷ11ｷ10ｷ9 ways to place the first 4 eggs in the
carton.

For each of those 12ｷ11ｷ10ｷ9 ways to place the 1st 4
eggs, there remain 8 places in the carton to place egg
#5. That&#39;s 12ｷ11ｷ10ｷ9ｷ8 ways to place the first 5 eggs in
the carton.

For each of those 12ｷ11ｷ10ｷ9ｷ8 ways to place the 1st 5
eggs, there remain 7 places in the carton to place egg
#6. That&#39;s 12ｷ11ｷ10ｷ9ｷ8ｷ7 ways to place the first 6 eggs
in the carton.

For each of those 12ｷ11ｷ10ｷ9ｷ8ｷ7 ways to place the 1st 6
eggs, there remain 6 places in the carton to place egg
#7. That&#39;s 12ｷ11ｷ10ｷ9ｷ8ｷ7ｷ6 ways to place the first 7
eggs in the carton.

For each of those 12ｷ11ｷ10ｷ9ｷ8ｷ7ｷ6 ways to place the 1st
7 eggs, there remain 5 places in the carton to place egg
#8. That&#39;s 12ｷ11ｷ10ｷ9ｷ8ｷ7ｷ6ｷ5 ways to place the first 8
eggs in the carton.

For each of those 12ｷ11ｷ10ｷ9ｷ8ｷ7ｷ6ｷ5 ways to place the
1st 8 eggs, there remain 4 places in the carton to place
egg #9. That&#39;s 12ｷ11ｷ10ｷ9ｷ8ｷ7ｷ6ｷ5ｷ4 ways to place the
first 9 eggs in the carton.

For each of those 12ｷ11ｷ10ｷ9ｷ8ｷ7ｷ6ｷ5ｷ4 ways to place the
1st 9 eggs, there remain 3 places in the carton to place
egg #10. That&#39;s 12ｷ11ｷ10ｷ9ｷ8ｷ7ｷ6ｷ5ｷ4ｷ3 ways to place the
first 10 eggs in the carton.

For each of those 12ｷ11ｷ10ｷ9ｷ8ｷ7ｷ6ｷ5ｷ4ｷ3 ways to place
the 1st 10 eggs, there remain 2 places in the carton to
place egg #11. That&#39;s 12ｷ11ｷ10ｷ9ｷ8ｷ7ｷ6ｷ5ｷ4ｷ3ｷ2 ways to
place the first 11 eggs in the carton.

For each of those 12ｷ11ｷ10ｷ9ｷ8ｷ7ｷ6ｷ5ｷ4ｷ3ｷ2 ways to place
the 1st 11 eggs, there remain only 1 place in the carton
to place egg #12. That&#39;s 12ｷ11ｷ10ｷ9ｷ8ｷ7ｷ6ｷ5ｷ4ｷ3ｷ2ｷ1 ways
to place all 12 eggs in the carton.

Answer: 12ｷ11ｷ10ｷ9ｷ8ｷ7ｷ6ｷ5ｷ4ｷ3ｷ2ｷ1 = 12!

That&#39;s also the number of permutations of 12 things taken all 12
at a time.    

nPn or P(n,n) = n!

Edwin&lt;/pre&gt;
 </PRE>