Solve the SYLLABUS Word Problem with Combinations | Homework Help

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Homework Help Overview

The problem involves calculating the number of different selections of 5 letters from the letters of the word SYLLABUS, which contains repeated letters.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss whether the selected letters must all be different and question how repeated letters should be treated in the counting process.

Discussion Status

Participants are exploring different interpretations of the problem, particularly regarding the treatment of repeated letters. Some guidance has been offered to review relevant course materials for clarification.

Contextual Notes

The problem does not explicitly state whether the selections must consist of all different letters, leading to uncertainty in how to approach the counting of combinations.

lionely
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Homework Statement



Calculate the numbers of different selections of 5 letters which can be made from the letters of the word SYLLABUS



Homework Equations





The Attempt at a Solution



I thought it would be 8C5 but that's not the answer.

Any help?
 
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lionely said:

Homework Statement



Calculate the numbers of different selections of 5 letters which can be made from the letters of the word SYLLABUS

I thought it would be 8C5 but that's not the answer.

Any help?

Do the five letters you select have to all be different? That would matter.
 
Well I don't think the question said that, so I don't think they would have to be all different.
 
If you say there are 8C5 different selections, here are two different ones. The first one is
YLABU
The second one is also
YLABU
but it's not the same as the first one.
What is different about them? Do you think they should be counted as different?
 
Would you count {Y,A,B,U,L} as two different selections if the L was the first L one time and the second L the next time?

[Edit] I see AlephZero asks the same question.
 
Hmmm, I don't think I would, the Ls are the same aren't they?
 
lionely said:
The Ls are the same aren't they?

Correct. The two S's are also the same.

Review your textbook or course notes for how that changes the answer, if you can't remember or figure it out for yourself.
 

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