SOLUTION: How many ways can the letters in the word smile be arranged if the first letter must be a vowel?

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Question 434741: How many ways can the letters in the word smile be arranged if the first letter must be a vowel?
Answer by Edwin McCravy(20055)   (Show Source): You can put this solution on YOUR website!
How many ways can the letters in the word smile be arranged if the first letter must be a vowel?
There are 2 vowels so there are 2 ways to choose the 1st letter.
For each of those 2 ways to choose the 1st letter there are 4 remaining
   letters to choose for the the 2nd letter.  That's 2*4 ways to choose
   the first 2 letters.
For each of those 2*4 ways to choose the 1st 2 letters there are 3 remaining
   letters to choose for the the 3rd letter.  That's 2*4*3 ways to choose
   the first 3 letters.
For each of those 2*4*3 ways to choose the 1st 3 letters there are 2 remaining
   letters to choose for the the 4th letter.  That's 2*4*3*2 ways to choose
   the first 4 letters.
For each of those 2*4*3*2 ways to choose the 1st 4 letters there is only 1
remaining letter to choose for the the 5th letter.  That's 2*4*3*2*1 ways to
choose all 5 letters.
 
So the answer is 2*4*3*2*1 = 48.  Here they all are:


1. EILMS
2. EILSM
3. EIMLS
4. EIMSL
5. EISLM
6. EISML
7. ELIMS
8. ELISM
9. ELMIS
10. ELMSI
11. ELSIM
12. ELSMI
13. EMILS
14. EMISL
15. EMLIS
16. EMLSI
17. EMSIL
18. EMSLI
19. ESILM
20. ESIML
21. ESLIM
22. ESLMI
23. ESMIL
24. ESMLI
25. IELMS
26. IELSM
27. IEMLS
28. IEMSL
29. IESLM
30. IESML
31. ILEMS
32. ILESM
33. ILMES
34. ILMSE
35. ILSEM
36. ILSME
37. IMELS
38. IMESL
39. IMLES
40. IMLSE
41. IMSEL
42. IMSLE
43. ISELM
44. ISEML
45. ISLEM
46. ISLME
47. ISMEL
48. ISMLE

Edwin
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