Question

video games how many different ways can 7 different video game cartridges be arranged on a shelf? use a graphing calculator. there are different ways to arrange 7 video game cartridges on a shelf.

Explanation:

Step1: Recall permutation of n distinct objects

The number of ways to arrange \( n \) distinct objects is given by \( n! \) (n factorial), where \( n! = n\times(n - 1)\times(n - 2)\times\cdots\times1 \). Here, \( n = 7 \), so we need to calculate \( 7! \).

Step2: Calculate \( 7! \)

\( 7! = 7\times6\times5\times4\times3\times2\times1 \)
First, \( 7\times6 = 42 \), then \( 42\times5 = 210 \), \( 210\times4 = 840 \), \( 840\times3 = 2520 \), \( 2520\times2 = 5040 \), \( 5040\times1 = 5040 \).

Answer:

5040