Question number 6.


How many ways can 5 students be assigned a seat in a classroom if there are 8 seats in a row?
 13


 56


 40


 40,320


 6,720


 None of the above.


Question number 7.


Suzy randomly picks marbles from a bag containing 18 identical marbles.  How many possible outcomes are there if she selects 2 marbles?
 153


 123


 133


 306


 143


 None of the above.

Let's solve each question one by one.

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### Question 6
*How many ways can 5 students be assigned a seat in a classroom if there are 8 seats in a row?*

This is a problem of selecting and arranging 5 students in 8 available seats, which requires a combination of selection and permutation.

1. **Choose 5 seats out of 8**: We can choose 5 seats from the 8 seats in \( \binom{8}{5} \) ways.
2. **Arrange 5 students in those 5 chosen seats**: For each selection of seats, we can arrange 5 students in \(5!\) (5 factorial) ways.

So, the total number of ways is:
\[
\binom{8}{5} \times 5! = \frac{8!}{5!(8-5)!} \times 5! = \frac{8!}{3!} = \frac{40,320}{6} = 6,720
\]

**Answer**: 6,720

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### Question 7
*Suzy randomly picks marbles from a bag containing 18 identical marbles. How many possible outcomes are there if she selects 2 marbles?*

Since the marbles are identical, any selection of 2 marbles will be indistinguishable from any other selection of 2 marbles. Thus, there is only **1 possible outcome** when picking 2 identical marbles.

**Answer**: None of the above

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Let me know if you'd like further details on either problem or a breakdown of any concepts. 

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### Related Questions
1. How many ways can 5 students be seated if the row has only 5 seats?
2. How would the answer change if the marbles were unique instead of identical?
3. What would the answer to question 6 be if the row had 10 seats instead of 8?
4. How would the calculation change in question 6 if each student had a specific seat preference?
5. If there were 20 identical marbles and Suzy could pick any number between 1 and 4, how many unique outcomes would there be?

#### Tip:
When calculating combinations and permutations, remember to distinguish between problems involving **identical** versus **unique** items, as this affects how outcomes are counted.

How many ways can 5 students be assigned a seat in a classroom if there are 8 seats in a row? How many possible outcomes are there if Suzy selects 2 marbles from a bag containing 18 identical marbles?

Explore how to calculate the number of ways to assign seats to 5 students out of 8 available and determine the outcomes when selecting identical marbles from a bag. Learn the use of combinations, permutations, and the Fundamental Counting Principle in solving these problems. Suitable for high school students in Grades 9-12.

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