Question

1. at the next game, the same 9 fans must be seated. home team fans must sit in the first five seats, and away team fans must sit in the last four seats. how many ways are there to arrange the 9 fans?

Explanation:

Step1: Calculate home fans arrangements

Home team fans (5) can be arranged in $5!$ ways: $5! = 5×4×3×2×1 = 120$

Step2: Calculate away fans arrangements

Away team fans (4) can be arranged in $4!$ ways: $4! = 4×3×2×1 = 24$

Step3: Total arrangements

Multiply both results: $120×24 = 2880$

Answer:

2880