Question

suppose there is a list of three jokes about books. in how many ways can these three jokes be ranked from best to worst?
the three jokes can be ranked from best to worst in \\(\square\\) different ways.
(simplify your answer. type a whole number.)

Explanation:

Step1: Identify the problem type

This is a permutation problem where we need to find the number of ways to arrange 3 distinct items (jokes) in order (from best to worst). The formula for permutations of \( n \) distinct objects is \( P(n, n)=\frac{n!}{(n - n)!}=n! \), where \( n!=n\times(n - 1)\times\cdots\times1 \). Here, \( n = 3 \).

Step2: Calculate the factorial

For \( n = 3 \), we calculate \( 3! \).
\( 3!=3\times2\times1 = 6 \).

Answer:

6