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