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 □ different five - sentence paragraphs that can be formed in this situation.

Explanation:

Step1: Calculate permutations

The formula for permutations of \(n\) distinct objects taken \(r\) at a time is \(P(n,r)=\frac{n!}{(n - r)!}\). Here, we have \(n = 5\) sentences and \(r=5\) (since we are forming paragraphs with all 5 sentences). But we have a fixed first - sentence ("He thought he saw a shape in the bushes") and a fixed last - sentence ("John looked out of the window"). So we are actually permuting the middle \(n=3\) sentences.
The number of permutations of \(n\) distinct objects is \(n!\). For \(n = 3\), the number of permutations is \(P(3,3)=\frac{3!}{(3 - 3)!}\). Since \(0!=1\) and \(3!=3\times2\times1 = 6\).

Answer:

6