Problem

A class has 34 students. In how many different ways can six students form a group for an activity? (Assume the order of the students is not important.)
There are different ways that the six students can form a group for an activity. (Type a whole number.)

Answer

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Answer

Final Answer: \(\boxed{1,344,904}\)

Steps

Step 1 :We are given a class of 34 students and we are asked to find out in how many different ways can six students form a group for an activity. The order of the students is not important.

Step 2 :This is a combination problem. The formula for combinations is: \[C(n, k) = \frac{n!}{k!(n-k)!}\] where n is the total number of items, k is the number of items to choose, and '!' denotes factorial, which is the product of all positive integers up to that number.

Step 3 :In this case, n = 34 (the total number of students) and k = 6 (the number of students to form a group).

Step 4 :Substituting the given values into the formula, we get: \[C(34, 6) = \frac{34!}{6!(34-6)!}\]

Step 5 :Solving the above expression, we find that there are 1,344,904 different ways that the six students can form a group for an activity.

Step 6 :Final Answer: \(\boxed{1,344,904}\)

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