Questions: 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"?

Solution Steps

To solve this problem, we need to determine the number of different ways to arrange the remaining three sentences between the fixed first and last sentences. This is a permutation problem where we are arranging 3 sentences.

We are given five sentences, and we need to form a paragraph that starts with "He thought he saw a shape in the bushes" and ends with "John looked out of the window." Thus, these two sentences are fixed in their positions.

The remaining sentences that can be arranged between the fixed sentences are:

1. "Mark had told him about the foxes."
2. "Could it be a fox?"
3. "However, nobody had seen one for months."

The number of ways to arrange the three remaining sentences is given by the factorial of the number of sentences, which is \(3!\): \[ 3! = 3 \times 2 \times 1 = 6 \]

Final Answer