How many ways can 4 students be selected from a class of 10? (2020)
Practice Questions
Q1
How many ways can 4 students be selected from a class of 10? (2020)
210
120
240
300
Questions & Step-by-Step Solutions
How many ways can 4 students be selected from a class of 10? (2020)
Step 1: Understand that we need to choose 4 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, where n is the total number of items (students) and r is the number of items to choose.
Step 4: The formula for combinations is nCr = n! / (r! * (n - r)!), where '!' denotes factorial, which is the product of all positive integers up to that number.
Step 5: In our case, n = 10 and r = 4. So we need to calculate 10C4.
Step 6: Plug the values into the formula: 10C4 = 10! / (4! * (10 - 4)!) = 10! / (4! * 6!).
Step 7: Calculate 10! = 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1, but we can simplify it by canceling out 6! in the denominator.
Step 8: This simplifies to 10 × 9 × 8 × 7 / (4 × 3 × 2 × 1).
Step 11: Divide the numerator by the denominator: 5040 / 24 = 210.
Step 12: Therefore, the number of ways to choose 4 students from 10 is 210.
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.
