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For part (b), where each of the 3 students chosen is assigned a different task, we need to calculate the number of permutations. This is because the order in which the students are assigned tasks matters.

To calculate the number of permutations of 3 students out of 13, we use the permutation formula:
\[ P(n, k) = \frac{n!}{(n - k)!} \]

Here, \( n = 13 \) and \( k = 3 \).

Let's compute this:
\[ P(13, 3) = \frac{13!}{(13 - 3)!} = \frac{13!}{10!} \]

We can simplify this by canceling out \( 10! \) from the numerator and the denominator:
\[ P(13, 3) = 13 \times 12 \times 11 \]

Now, calculate the result:
\[ 13 \times 12 \times 11 = 1716 \]

So, there are 1716 ways an adviser can choose and assign 3 students from a class of 13 if they are each given a different task.

Would you like more details or have any questions? Here are 5 more questions you might find interesting to ask:

1. How many ways can an adviser choose 5 students from a class of 13 if they are all assigned the same task?
2. How many permutations are there if the adviser needs to assign different tasks to 4 students from a class of 13?
3. Can you explain the difference between a combination and a permutation with an example?
4. How do you calculate the number of combinations if there are 20 students and the adviser needs to choose 5?
5. What are some real-life applications of permutations and combinations?

**Tip:** Remember that when calculating permutations, the order of selection matters, whereas in combinations, it does not.

Learn how to calculate permutations when choosing 3 students from a class of 13 to ensure each student gets a different task. This problem involves using the permutation formula and understanding how order matters in selection. Suitable for high school students studying permutations.

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