Question

you need to arrange ten of your favorite books along a small shelf. how many different ways can you arrange the books, assuming that the order of the books makes a difference to you?

(□ ways
type a whole number.)

Explanation:

Step1: Use permutation formula

The number of permutations of \(n\) distinct objects is \(n!\). Here \(n = 10\) (the number of books).

Step2: Calculate \(n!\)

\(n!=n\times(n - 1)\times\cdots\times1\). So \(10!=10\times9\times8\times7\times6\times5\times4\times3\times2\times1\).
\(10\times9 = 90\), \(90\times8=720\), \(720\times7 = 5040\), \(5040\times6=30240\), \(30240\times5 = 151200\), \(151200\times4=604800\), \(604800\times3=1814400\), \(1814400\times2=3628800\), \(3628800\times1=3628800\).

Answer:

\(3628800\)