Problem

A group of 6 students is to be chosen from a 29-member class to represent the class on the student council. How many ways can this be done? (NOTE: Order of the selection is not important.) Answer: ways Question Help: Video Message instructor

Solution

Step 1 :This is a combination problem. We are choosing 6 students from a group of 29, and the order in which we choose them does not matter. 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 (the product of all positive integers up to that number). In this case, n=29 and k=6.

Step 2 :Substitute n = 29 and k = 6 into the formula, we get \[C(29, 6) = \frac{29!}{6!(29-6)!}\]

Step 3 :Calculate the above expression, we get 475020.0

Step 4 :So, there are \(\boxed{475020}\) ways to choose 6 students from a 29-member class to represent the class on the student council.

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Source: https://solvelyapp.com/problems/OEUtOdLCD6/

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