How many ways can 3 students be selected from a group of 10?
Practice Questions
Q1
How many ways can 3 students be selected from a group of 10?
120
90
100
80
Questions & Step-by-Step Solutions
How many ways can 3 students be selected from a group of 10?
Step 1: Understand that we want to choose 3 students from a total of 10 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: The formula for combinations is given by 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 our case, n = 10 (total students) and r = 3 (students to select).
Step 5: Plug the values into the formula: 10C3 = 10! / (3! * (10 - 3)!) = 10! / (3! * 7!).
Step 6: Calculate 10! = 10 × 9 × 8 × 7!, so we can simplify: 10C3 = (10 × 9 × 8) / (3 × 2 × 1).
Step 9: Divide the numerator by the denominator: 720 / 6 = 120.
Step 10: Conclude that there are 120 different ways to select 3 students from a group of 10.
Combinatorics – The question tests the understanding of combinations, specifically how to calculate the number of ways to choose a subset from a larger set without regard to the order of selection.
