Question

ellie is organizing textbooks on her bookshelf. she has an english textbook, a biology textbook, a history textbook, and a writing textbook. how many different ways can she line the textbooks up on her bookshelf?

Explanation:

Step1: Identify the problem type

This is a permutation problem where we need to find the number of ways to arrange \( n \) distinct objects. The formula for permutations of \( n \) distinct objects is \( n! \) (n factorial), where \( n! = n\times(n - 1)\times(n - 2)\times\cdots\times1 \). Here, Ellie has 4 distinct textbooks, so \( n = 4 \).

Step2: Calculate the factorial

For \( n = 4 \), we calculate \( 4! \).
\( 4! = 4\times3\times2\times1 \)
First, \( 4\times3 = 12 \). Then, \( 12\times2 = 24 \). Finally, \( 24\times1 = 24 \).

Answer:

24