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

The problem is asking how many different lineups are possible when selecting all 7 songs from a list of 7 songs. This is a permutation problem since the order of the songs in the lineup matters.

The number of permutations of \( n \) objects taken \( n \) at a time is given by:

\[
P(n, n) = n!
\]

In this case, \( n = 7 \), so we need to compute \( 7! \):

\[
7! = 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 5040
\]

Therefore, the number of different possible lineups is \( 5040 \).

### Summary:
There are **5040** different possible lineups for the 7 songs.

Would you like further details or have any questions?

Here are 5 related questions you might be interested in:
1. What if only 5 songs are selected from the list of 7? How many lineups are possible?
2. How does the number of lineups change if the order of songs doesn't matter?
3. What if 10 songs were available, but only 7 needed to be selected for the lineup?
4. How many ways are there to arrange 7 songs if no song can be repeated?
5. What if one of the songs must always be placed at the beginning of the lineup?

**Tip**: Permutations account for order, while combinations ignore it!

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

Discover how to calculate the number of possible lineups when selecting 7 songs from a list of 7. This problem explores permutation concepts and factorials, suitable for students in Grades 9-12. Learn how to use the formula P(n, n) = n! for a detailed step-by-step solution.

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