SOLUTION: How many ways can you order the letters in SASKATOON if the first two letters must both be an A and the last letter must be a K?

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Question 1170027: How many ways can you order the letters in SASKATOON if the first two letters must both be an A and the last letter must be a K?
Found 3 solutions by greenestamps, math_helper, ikleyn:
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


That leaves the letters SSTOON in the middle -- 6 letters including 2 pairs. The number of ways of arranging those letters is

6%21%2F%28%282%21%29%282%21%29%29+=+720%2F4+=+180

Then the two A's in the first two positions can be arranged in either of 2 ways.

ANSWER: 180*2 = 360 different ways.

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Corrected response....

Yes, the other tutors are right -- we are talking about distinguishable orderings, so there is only 1 ordering of the two A's at the beginning.

ANSWER: 180*1 = 180 different ways

Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
@greenestamps: shouldn't the A's be treated as indistinguishable? If so, the answer is simply 180.

Answer by ikleyn(52780) About Me  (Show Source):
You can put this solution on YOUR website!
.

First, the question is posed incorrectly.

The correct version is THIS: 

    In how many highlight%28distinguished%29 ways can you order the letters in SASKATOON 

    if the first two letters must both be an A and the last letter must be a K?


Secondly, the correct answer is 180.

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To see many similar solved problems, look into the lesson
    - Arranging elements of sets containing indistinguishable elements
in this site.

Also,  you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic  "Combinatorics: Combinations and permutations".


Save the link to this textbook together with its description

Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson

into your archive and use when it is needed.