A student downloaded 6 music files to a portable music player. In how many different orders can the songs be played?
Question
A student downloaded 6 music files to a portable music player. In how many different orders can the songs be played?
Solution
This is a permutation problem. The number of ways to arrange n distinct objects in a row is given by the formula n!.
In this case, the student has 6 music files, so n = 6.
Step 1: Identify the number of objects to arrange, which is 6 in this case.
Step 2: Use the formula for permutations of n objects, which is n!.
Step 3: Calculate the factorial of the number of objects.
The factorial of a number is the product of all positive integers less than or equal to that number.
So, 6! = 6 * 5 * 4 * 3 * 2 * 1 = 720.
Therefore, the student can play the 6 music files in 720 different orders.
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