How many ways can 4 people be selected from a group of 12?

How many ways can 4 people be selected from a group of 12?

Correct Answer: 495

Step 1: Understand that we want to choose 4 people from a group of 12.
Step 2: Recognize that the order in which we select the people does not matter. This means we will use combinations, not permutations.
Step 3: The formula for combinations is C(n, r) = 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 and r = 4. So we will calculate C(12, 4).
Step 5: Calculate 12! (which is 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1).
Step 6: Calculate 4! (which is 4 x 3 x 2 x 1).
Step 7: Calculate (12 - 4)! = 8! (which is 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1).
Step 8: Plug these values into the combination formula: C(12, 4) = 12! / (4! * 8!).
Step 9: Simplify the calculation to find the number of ways to choose 4 people from 12.
Step 10: The final answer 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.