# Solve the SYLLABUS Word Problem with Combinations | Homework Help

• lionely
In summary, the number of different selections of 5 letters that can be made from the word "SYLLABUS" is not 8C5. The answer is affected by the fact that some of the letters are repeated, and the selection does not have to include all different letters. Further review of course materials may be necessary to determine the correct answer.
lionely

## Homework Statement

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

## The Attempt at a Solution

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

Any help?

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?

 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.

## 1. How do combinations apply to solving syllabus word problems?

Combinations are used in solving syllabus word problems when the problem involves selecting a specific number of items from a larger group of items, without regard to the order in which they are selected.

## 2. What is the formula for solving a combination problem?

The formula for calculating the number of combinations is nCr = n! / r!(n-r)!, where n is the total number of items and r is the number of items being selected.

## 3. Can you provide an example of solving a syllabus word problem using combinations?

Sure, for example, if a syllabus lists 10 topics and a student must choose 3 topics to study for an exam, the number of possible combinations is 10C3 = 10! / 3!(10-3)! = 120. This means there are 120 different ways the student can choose 3 topics from the 10 listed.

## 4. Are there any common mistakes to avoid when using combinations to solve syllabus word problems?

One common mistake is forgetting to use the combination formula and instead using the permutation formula, which is used when the order of the selected items matters. It's important to carefully read the problem and determine whether combinations or permutations should be used.

## 5. Can combinations also be used in real-life scenarios outside of syllabus word problems?

Yes, combinations are used in many real-life scenarios such as lottery games, selecting a team for a sports tournament, and creating a password with a specific number of characters. Any situation that involves selecting a specific number of items from a larger group without considering the order can be solved using combinations.

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