In how many ways can 3 students be chosen from a group of 8? (2015)

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Q: In how many ways can 3 students be chosen from a group of 8? (2015)

Solution: The number of ways to choose 3 students from 8 is 8C3 = 56.

Steps: 12

Step 1: Understand that we need to choose 3 students from a total of 8 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, which is written as nCr, where n is the total number of items (students) and r is the number of items to choose. The formula is nCr = n! / (r! * (n - r)!).
Step 4: In this case, n = 8 (total students) and r = 3 (students to choose). So we will calculate 8C3.
Step 5: Plug the values into the formula: 8C3 = 8! / (3! * (8 - 3)!) = 8! / (3! * 5!).
Step 6: Calculate 8! = 8 × 7 × 6 × 5! (we can stop at 5! because it will cancel out).
Step 7: Calculate 3! = 3 × 2 × 1 = 6.
Step 8: Now substitute back into the equation: 8C3 = (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, the number of ways to choose 3 students from 8 is 56.