How many ways can you select 3 students from a group of 8?

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Question: How many ways can you select 3 students from a group of 8?

Options:

Correct Answer: 84

Solution:

The number of combinations of 3 students from 8 is C(8, 3) = 8! / (3!(8-3)!) = 56.

How many ways can you select 3 students from a group of 8?

How many ways can you select 3 students from a group of 8?

Step 1: Understand that we want to choose 3 students from a total of 8 students.
Step 2: Recognize that the order in which we select the students does not matter. This means we will use combinations, not permutations.
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 our case, n = 8 (total students) and r = 3 (students to choose). So we will calculate C(8, 3).
Step 5: Plug the values into the formula: C(8, 3) = 8! / (3!(8 - 3)!).
Step 6: Simplify the formula: C(8, 3) = 8! / (3! * 5!).
Step 7: Calculate 8! = 8 × 7 × 6 × 5!, so we can cancel 5! in the numerator and denominator.
Step 8: Now we have C(8, 3) = (8 × 7 × 6) / (3 × 2 × 1).
Step 9: Calculate the numerator: 8 × 7 × 6 = 336.
Step 10: Calculate the denominator: 3 × 2 × 1 = 6.
Step 11: Divide the numerator by the denominator: 336 / 6 = 56.
Step 12: Therefore, there are 56 different ways to select 3 students from a group of 8.

Combinations – The concept of selecting items from a larger set where the order does not matter, calculated using the formula C(n, r) = n! / (r!(n-r)!)