A coordinator will select 7 songs from a list of 8 songs to compose an event's musical entertainment lineup.  How many different lineups are possible?

To solve this problem, we need to determine how many ways we can select 7 songs from a list of 8 songs.

Since the order in which the songs are selected does not matter, we are dealing with a **combination** problem, not a permutation problem.

The formula for combinations is:

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

Where:
- \( n \) is the total number of items (8 songs),
- \( r \) is the number of items to choose (7 songs).

Now, let's substitute the values into the formula:

\[
C(8, 7) = \frac{8!}{7!(8 - 7)!} = \frac{8!}{7!1!}
\]

Since \( 8! = 8 \times 7! \), we can cancel out the \( 7! \) terms:

\[
C(8, 7) = \frac{8 \times 7!}{7! \times 1!} = 8
\]

Thus, there are **8 different lineups** possible.

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Would you like more details, or do you have any questions?

Here are 5 related questions to expand on this concept:

1. What if the coordinator selects 6 songs instead of 7 from the 8 songs? How many lineups are possible?
2. If the order of the songs mattered, how would you calculate the number of different lineups?
3. How many ways can the coordinator select 3 songs from the list of 8 songs?
4. What if the coordinator can select any number of songs between 1 and 8? How would you compute the total number of possible lineups?
5. What if 2 songs must always be selected together? How many lineups are possible under this condition?

**Tip:** For combination problems, remember that order does not matter, while for permutation problems, the sequence is important.

A coordinator will select 7 songs from a list of 8 songs to compose an event's musical entertainment lineup. How many different lineups are possible?

Learn how to calculate the number of ways to select 7 songs from a list of 8 using combinations. This step-by-step guide covers the combination formula C(n, r) and its application. Suitable for students in Grades 9-12.

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