How many different ways can 4 students be selected from a class of 10?

How many different ways can 4 students be selected from a class of 10?

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: In this case, n = 10 (total students) and r = 4 (students to choose). So we need to calculate 10C4.
Step 5: The formula for combinations is nCr = n! / (r! * (n - r)!), where '!' denotes factorial (the product of all positive integers up to that number).
Step 6: Calculate 10! (10 factorial), which is 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1.
Step 7: Calculate 4! (4 factorial), which is 4 x 3 x 2 x 1.
Step 8: Calculate (10 - 4)! = 6!, which is 6 x 5 x 4 x 3 x 2 x 1.
Step 9: Plug these values into the combination formula: 10C4 = 10! / (4! * 6!).
Step 10: Simplify the calculation to find the total number of ways to choose 4 students from 10, which equals 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.