SOLUTION: In how many different ways can the letters of "SUNDAY" be arranged? How many of these arrangements begin with an "S"? How many begin with "S" but do not end with a vowel?

Algebra ->  Permutations -> SOLUTION: In how many different ways can the letters of "SUNDAY" be arranged? How many of these arrangements begin with an "S"? How many begin with "S" but do not end with a vowel?      Log On


   

Question 1143486: In how many different ways can the letters of "SUNDAY" be arranged?
How many of these arrangements begin with an "S"?
How many begin with "S" but do not end with a vowel?
Found 3 solutions by Edwin McCravy, Alan3354, ikleyn:
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
In how many different ways can the letters of "SUNDAY" be arranged?
6 choices for the 1st letter, "S,U,N,D,A,Y" for which there are
5 choices for the 2nd letter, for which there are
4 choices for the 3rd letter, for which there are
3 choices for the 4th letter, for which there are
2 choices for the 5th letter, for which there are
1 choice for the 6th letter.

That's 6∙5∙4∙3∙2∙1 = 6! = 720 ways

How many of these arrangements being with "S"? 
1 choice for the 1st letter, "S", for which there are
5 choices for the 2nd letter, "U,N,D,A,Y", for which there are
4 choices for the 3rd letter, for which there are
3 choices for the 4th letter, for which there are
2 choices for the 5th letter, for which there are
1 choice for the 6th letter.

That's 1∙5∙4∙3∙2∙1 = 1∙5! = 120 ways

How many begin with "S" but do not end with vowel?
1 choice for the 1st letter, "S", for which there are
2 choices for the 6th letter, "U,A", for which there are
4 choices for the 2nd letter, for which there are
3 choices for the 3rd letter, for which there are
2 choices for the 4th letter, for which there are
1 choice for the 5th letter.

That's 1∙2∙4∙3∙2∙1 = 2∙4! = 4∙24 = 96 ways

Edwin

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
In how many different ways can the letters of "SUNDAY" be arranged?
-----------
The 1st letter is 1 of 6.
Then 1 of 5, etc.
----> 6*5*4*3*2*1 = 720 ways.
==============================================
How many of these arrangements being with an "S"?
720/6 = 120 ways.
=============================
I was interrupted. When I came back to finish, there were 2 other submissions already.

Answer by ikleyn(52787) About Me  (Show Source):
You can put this solution on YOUR website!
.

            The solution by Edwin is good,  but the last part of the solution has to be edited.

            This editing is below.



How many begin with  "S"  but do not end with vowel? 

1 choice for the 1st letter, "S", for which there are
2 choices for the 6th letter, "N,D", for which there are
4 choices for the 2nd letter, for which there are
3 choices for the 3rd letter, for which there are
2 choices for the 4th letter, for which there are
1 choice for the 5th letter.


That's  1∙2∙4∙3∙2∙1 = 2∙4! = 2∙24 = 48 ways.      ANSWER