Final answer:
To calculate the number of ways an examinee can answer five questions, selecting at least one from each part A, B, and C of a math exam, we use combinations.
By fixing one question from each part and then choosing the remaining two from the leftover questions, we conclude there are 2304 ways to select five questions.
Step-by-step explanation:
The student's question asks about the number of ways an examinee can answer five questions in a math exam when they have to select at least one question from each part A, B, and C of the exam paper.
Since there are four questions in each part, we can use combinations to find the possible ways to select the questions. Here's how to calculate this:
- Select one question from each part: This is a fixed condition, so we begin by selecting one question from part A, one from B, and one from C. This gives us 4C1 × 4C1 × 4C1 combinations.
- Now we have to select two more questions from the remaining 9 (since three questions have already been selected). There are 9C2 ways to do this.
- Therefore, the total number of ways to select five questions with at least one from each part is the product of these two combinations: 4C1 × 4C1 × 4C1 × 9C2.
- Calculation: 4 × 4 × 4 × 36 = 2304 ways.
So, the examinee can answer five questions in 2304 different ways while selecting at least one from each part.