How many ways can you choose 4 students from a class of 12?

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Question: How many ways can you choose 4 students from a class of 12?

Options:

Correct Answer: 495

Solution:

The number of ways to choose 4 students from 12 is C(12, 4) = 495.

How many ways can you choose 4 students from a class of 12?

How many ways can you choose 4 students from a class of 12?

Step 1: Understand that we want to choose 4 students from a total of 12 students.
Step 2: Recognize that this is a combination problem because the order in which we choose the students does not matter.
Step 3: Use the combination formula C(n, r) = n! / (r! * (n - r)!), where n is the total number of items (students) and r is the number of items to choose.
Step 4: In this case, n = 12 and r = 4. So we will calculate C(12, 4).
Step 5: Plug the values into the formula: C(12, 4) = 12! / (4! * (12 - 4)!) = 12! / (4! * 8!).
Step 6: Calculate 12! = 12 × 11 × 10 × 9 × 8! (we can stop at 8! because it will cancel out).
Step 7: Now we have C(12, 4) = (12 × 11 × 10 × 9) / (4 × 3 × 2 × 1).
Step 8: Calculate the numerator: 12 × 11 × 10 × 9 = 11880.
Step 9: Calculate the denominator: 4 × 3 × 2 × 1 = 24.
Step 10: Divide the numerator by the denominator: 11880 / 24 = 495.
Step 11: Therefore, the number of ways to choose 4 students from 12 is 495.

Combinatorics – The study of counting, specifically the selection of items from a larger set without regard to the order of selection.
Binomial Coefficient – The formula C(n, k) = n! / (k!(n-k)!) used to calculate the number of ways to choose k items from n items.