For a segment of a radio​ show, a disc jockey can play 7 records. If there are 11 records to select​ from, in how many ways can the program for this segment be​ arranged?
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To find the number of ways to arrange 7 records from a selection of 11, we use permutations since the order matters. The formula for permutations is:

\[
P(n, r) = \frac{n!}{(n - r)!}
\]

where \( n \) is the total number of items (11 records), and \( r \) is the number of items to arrange (7 records).

Calculating this:

\[
P(11, 7) = \frac{11!}{(11 - 7)!} = \frac{11!}{4!} = \frac{11 \times 10 \times 9 \times 8}{1} = 7920
\]

So, there are **7,920 ways** to arrange the program for this segment.

Would you like more details or have any questions? Here are some related questions to consider:

1. How does this calculation change if we choose 5 records instead of 7?
2. What if the order of the records didn't matter?
3. How would you approach a similar problem with more than 11 records?
4. What is the concept of combinations, and how does it differ from permutations?
5. Can you provide an example of a real-life situation where you would need to calculate arrangements like this? 

**Tip:** Always clarify whether the order of selection matters to determine if you should use permutations or combinations.

For a segment of a radio show, a disc jockey can play 7 records. If there are 11 records to select from, in how many ways can the program for this segment be arranged?

Learn how to calculate the number of ways to arrange 7 records out of 11 using permutations. This detailed step-by-step solution explains the permutation formula P(n, r) = n! / (n - r)! and applies it to a real-world example. Perfect for students in Grades 10-12 studying combinatorics.

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