How many ways can 4 students be selected from a group of 12? (2014)

How many ways can 4 students be selected from a group of 12? (2014)

Step 1: Understand that we want to choose 4 students from a total of 12 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 our case, n = 12 (total students) and r = 4 (students to select).
Step 5: Plug the values into the formula: 12C4 = 12! / (4! * (12 - 4)!) = 12! / (4! * 8!).
Step 6: Calculate 12! (which is 12 x 11 x 10 x 9 x 8!) and notice that the 8! in the numerator and denominator will cancel out.
Step 7: Now we have: 12C4 = (12 x 11 x 10 x 9) / (4 x 3 x 2 x 1).
Step 8: Calculate the numerator: 12 x 11 x 10 x 9 = 11880.
Step 9: Calculate the denominator: 4 x 3 x 2 x 1 = 24.
Step 10: Divide the numerator by the denominator: 11880 / 24 = 495.
Step 11: Therefore, the number of ways to select 4 students from 12 is 495.

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.