Question

use the five sentences below to answer the question.
mark had told him about the foxes.
john looked out of the window.
could it be a fox?
however, nobody had seen one for months.
he thought he saw a shape in the bushes.
how many different five - sentence paragraphs can be formed if the paragraph begins with \he thought he saw a shape in the bushes\ and ends with \john looked out of the window\?
there are \\(\square\\) different five - sentence paragraphs that can be formed in this situation.

Explanation:

Step1: Determine the number of permutations

We have 5 sentences. The first sentence is fixed as "He thought he saw a shape in the bushes" and the last sentence is fixed as "John looked out of the window". So we need to find the number of ways to arrange the remaining 3 sentences ("Mark had told him about the foxes", "However, nobody had seen one for months", "Could it be a fox?") in the middle.
The number of permutations of \(n\) distinct objects is \(n!\). Here \(n = 3\).
The formula for permutations of \(n\) objects is \(P(n,n)=\frac{n!}{(n - n)!}=n!\)
For \(n=3\), we have \(3! = 3\times2\times1\)

Step2: Calculate the value

\(3\times2\times1=6\)

Answer:

6