In how many ways can 3 students be selected from a class of 8 to represent in a competition?

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Q: In how many ways can 3 students be selected from a class of 8 to represent in a competition?

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

Steps: 13

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 of selection 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.
Step 4: In this case, n = 8 (total students) and r = 3 (students to choose).
Step 5: The combination formula is nCr = n! / (r! * (n - r)!), where '!' denotes factorial, which is the product of all positive integers up to that number.
Step 6: Calculate 8C3 using the formula: 8C3 = 8! / (3! * (8 - 3)!)
Step 7: Simplify the calculation: 8C3 = 8! / (3! * 5!)
Step 8: Calculate 8! = 8 × 7 × 6 × 5! (we can cancel 5! in the numerator and denominator)
Step 9: Now we have 8C3 = (8 × 7 × 6) / (3 × 2 × 1)
Step 10: Calculate the numerator: 8 × 7 × 6 = 336
Step 11: Calculate the denominator: 3 × 2 × 1 = 6
Step 12: Divide the numerator by the denominator: 336 / 6 = 56
Step 13: Therefore, there are 56 different ways to choose 3 students from 8.