<PRE><B>Question 33697</B>
&lt;pre&gt;&lt;font size = 4&gt;&lt;b&gt;how many different ways can you write the following using 
probability, permutations or combinations
a&lt;sup&gt;4&lt;/sup&gt;b&lt;sup&gt;2&lt;/sup&gt;c&lt;sup&gt;5&lt;/sup&gt;d
There are four factors a&lt;sup&gt;4&lt;/sup&gt;, b&lt;sup&gt;2&lt;/sup&gt;, c&lt;sup&gt;5&lt;/sup&gt;, and d.  
There are 4 choices of factors to go first. 

Then for each of those 4 possible ways to choose the 
first factor, there are 3 factors remaining to choose 
for the 2nd factor. That&#39;s 4×3 or 12 ways to choose 
the first two factors.

Then for each of those 4×3 or 12 possible ways to choose 
the first two factors, there are 2 factors remaining to 
choose for the 3rd factor. That&#39;s 4×3×2 or 24 ways to choose 
the first three factors.

Then for each of those 4×3×2 or 24 possible ways to choose 
the first two factors, there is only 1 factor remaining to 
choose for the 4th factor. That&#39;s 4×3×2×1, or still 24 ways 
to choose the first four factors.

It can also be called 4! or &quot;the number of permutations of 4
things taken 4 at a time.

These are

 1. a&lt;sup&gt;4&lt;/sup&gt;b&lt;sup&gt;2&lt;/sup&gt;c&lt;sup&gt;5&lt;/sup&gt;d 
 2. a&lt;sup&gt;4&lt;/sup&gt;b&lt;sup&gt;2&lt;/sup&gt;dc&lt;sup&gt;5&lt;/sup&gt; 
 3. a&lt;sup&gt;4&lt;/sup&gt;c&lt;sup&gt;5&lt;/sup&gt;b&lt;sup&gt;2&lt;/sup&gt;d
 4. a&lt;sup&gt;4&lt;/sup&gt;c&lt;sup&gt;5&lt;/sup&gt;db&lt;sup&gt;2&lt;/sup&gt;            
 5. a&lt;sup&gt;4&lt;/sup&gt;db&lt;sup&gt;2&lt;/sup&gt;c&lt;sup&gt;5&lt;/sup&gt;                         
 6. a&lt;sup&gt;4&lt;/sup&gt;dc&lt;sup&gt;5&lt;/sup&gt;b&lt;sup&gt;2&lt;/sup&gt;                         
 7. b&lt;sup&gt;2&lt;/sup&gt;a&lt;sup&gt;4&lt;/sup&gt;c&lt;sup&gt;5&lt;/sup&gt;d             
 8. b&lt;sup&gt;2&lt;/sup&gt;a&lt;sup&gt;4&lt;/sup&gt;dc&lt;sup&gt;5&lt;/sup&gt;             
 9. b&lt;sup&gt;2&lt;/sup&gt;c&lt;sup&gt;5&lt;/sup&gt;a&lt;sup&gt;4&lt;/sup&gt;d
10. b&lt;sup&gt;2&lt;/sup&gt;c&lt;sup&gt;5&lt;/sup&gt;da&lt;sup&gt;4&lt;/sup&gt;
11. b&lt;sup&gt;2&lt;/sup&gt;da&lt;sup&gt;4&lt;/sup&gt;c&lt;sup&gt;5&lt;/sup&gt;
12. b&lt;sup&gt;2&lt;/sup&gt;dc&lt;sup&gt;5&lt;/sup&gt;a&lt;sup&gt;4&lt;/sup&gt;
13. c&lt;sup&gt;5&lt;/sup&gt;a&lt;sup&gt;4&lt;/sup&gt;b&lt;sup&gt;2&lt;/sup&gt;d
14. c&lt;sup&gt;5&lt;/sup&gt;a&lt;sup&gt;4&lt;/sup&gt;db&lt;sup&gt;2&lt;/sup&gt;
15. c&lt;sup&gt;5&lt;/sup&gt;b&lt;sup&gt;2&lt;/sup&gt;a&lt;sup&gt;4&lt;/sup&gt;d
16. c&lt;sup&gt;5&lt;/sup&gt;b&lt;sup&gt;2&lt;/sup&gt;da&lt;sup&gt;4&lt;/sup&gt;
17. c&lt;sup&gt;5&lt;/sup&gt;da&lt;sup&gt;4&lt;/sup&gt;b&lt;sup&gt;2&lt;/sup&gt;
18. c&lt;sup&gt;5&lt;/sup&gt;db&lt;sup&gt;2&lt;/sup&gt;a&lt;sup&gt;4&lt;/sup&gt;
19. da&lt;sup&gt;4&lt;/sup&gt;b&lt;sup&gt;2&lt;/sup&gt;c&lt;sup&gt;5&lt;/sup&gt;
20. da&lt;sup&gt;4&lt;/sup&gt;c&lt;sup&gt;5&lt;/sup&gt;b&lt;sup&gt;2&lt;/sup&gt;
21. db&lt;sup&gt;2&lt;/sup&gt;a&lt;sup&gt;4&lt;/sup&gt;c&lt;sup&gt;5&lt;/sup&gt;
22. db&lt;sup&gt;2&lt;/sup&gt;c&lt;sup&gt;5&lt;/sup&gt;a&lt;sup&gt;4&lt;/sup&gt;
23. dc&lt;sup&gt;5&lt;/sup&gt;a&lt;sup&gt;4&lt;/sup&gt;b&lt;sup&gt;2&lt;/sup&gt;
24. dc&lt;sup&gt;5&lt;/sup&gt;b&lt;sup&gt;2&lt;/sup&gt;a&lt;sup&gt;4&lt;/sup&gt;

Edwin 
AnlytcPhil@aol.com&lt;/pre&gt;</PRE>