Problem

A group of 4 students is selected from a group of 17 students to take part in a class in cell biology. Complete parts (a) and (b) below.
(a) In how many ways can this be done?

There are possible ways.
(b) In how many ways will the group who will not take part be chosen?

There are possible ways.

Answer

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Answer

Final Answer: There are 2380 possible ways to select 4 students from a group of 17 for the class, and there are also 2380 possible ways to select the group of 13 students who will not take part in the class.

Steps

Step 1 :The problem is asking for the number of ways to select a group of 4 students from a group of 17 students. This is a combination problem, as the order of selection does not matter. The formula for combinations is given by: C(n,k)=n!k!(nk)! where n is the total number of items, k is the number of items to choose, and '!' denotes factorial.

Step 2 :For part (a), n = 17 (the total number of students) and k = 4 (the number of students to select for the class).

Step 3 :For part (b), the group who will not take part will be the remaining students after the 4 students have been selected. This means we are choosing 17 - 4 = 13 students from the group of 17. So, for this part, n = 17 and k = 13.

Step 4 :Calculating these values, we find that there are 2380 ways to select 4 students from a group of 17, and the same number of ways to select the remaining 13 students.

Step 5 :This makes sense, as choosing 4 students to participate is equivalent to choosing 13 students not to participate.

Step 6 :Final Answer: There are 2380 possible ways to select 4 students from a group of 17 for the class, and there are also 2380 possible ways to select the group of 13 students who will not take part in the class.

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