SOLUTION: Find the number of words that can be made from the letters P,Q,R and S by using any number of letters without repeating any letter.

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Question 832231: Find the number of words that can be made from the letters P,Q,R and S by using any number of letters without repeating any letter.
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
We can pick the 1st letter any of 4 ways.
For each of those ways to pick the 1st letter,
there are 3 remaining letters we can pick for the 2nd letter.
So that's 4×3 ways to pick the first two letters.
For each of those 4×3 ways to pick the first 2 letter,
there are 2 remaining letters we can pick for the 3rd letter.
So that's 4×3×2 ways to pick the first three letters.
Now there is only 1 letter remaining to pick for the 4th 
letter.
So the answer is 4×3×2×1 which is called "4 factorial" and is written 4!
and when we multiply it out we get 4×3×2×1 = 24.  So there are 24
ways to arrange those four letters in different orders.
Here's a check:

1. PQRS
2. PQSR
3. PRQS
4. PRSQ
5. PQRS
6. PQSR
7. QPRS
8. QPSR
9. QRPS
10. QRSP
11. QPRS
12. QPSR
13. RQPS
14. RQSP
15. RPQS
16. RPSQ
17. RQPS
18. RQSP
19. SQRP
20. SQPR
21. SRQP
22. SRPQ
23. SQRP
24. SQPR
  
Yes there are 24.  But for many problems there are too many to check.

Edwin