In how many ways can 3 students be selected from a class of 10?

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Question: In how many ways can 3 students be selected from a class of 10?

Options:

Correct Answer: 120

Solution:

The number of ways to choose 3 students from 10 is given by 10C3 = 120.

In how many ways can 3 students be selected from a class of 10?

In how many ways can 3 students be selected from a class of 10?

Step 1: Understand that we need to choose 3 students from a total of 10 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 = n! / (r! * (n - r)!), where n is the total number of items, r is the number of items to choose, and '!' denotes factorial.
Step 4: In this case, n = 10 (total students) and r = 3 (students to choose).
Step 5: Plug the values into the formula: 10C3 = 10! / (3! * (10 - 3)!)
Step 6: Simplify the formula: 10C3 = 10! / (3! * 7!)
Step 7: Calculate 10! = 10 × 9 × 8 × 7! (we can cancel 7! in the numerator and denominator).
Step 8: Now we have: 10C3 = (10 × 9 × 8) / (3 × 2 × 1).
Step 9: Calculate the numerator: 10 × 9 × 8 = 720.
Step 10: Calculate the denominator: 3 × 2 × 1 = 6.
Step 11: Divide the numerator by the denominator: 720 / 6 = 120.
Step 12: Conclude that there are 120 different ways to choose 3 students from a class of 10.

Combinatorics – The study of counting, specifically how to choose a subset of items from a larger set without regard to the order of selection.
Binomial Coefficient – The formula used to calculate the number of ways to choose k items from n items, denoted as nCk or C(n, k).