A committee of 4 people is to be formed from a group of 9 distinct people. If there are no additional restrictions, in how many different ways can this 4-person committee be chosen?

Introduction / Context:
This is a straightforward combinations question about forming a committee. We want to choose a subset of people from a larger group, and the order in which they are chosen does not matter. Problems of this kind occur frequently in selection scenarios like committee formation, project teams, or representative groups.

Given Data / Assumptions:

• Total people available: 9 distinct individuals.
• Number of people needed in the committee: 4.
• There are no special roles like president or secretary; all committee members are equal.
• Order of selection does not matter; a set of 4 people is counted once.
• No person can be selected more than once.

Concept / Approach:
When selecting r people from n distinct individuals and only the set of chosen people matters, we use combinations. The formula is:
nCr = n! / (r! * (n - r)!). Here, n = 9 and r = 4. So we compute 9C4 to find the total number of possible 4 person committees.

Step-by-Step Solution:
Step 1: Identify that n = 9 and r = 4. Step 2: Apply the combination formula: 9C4 = 9! / (4! * 5!). Step 3: Express 9! / 5! as 9 * 8 * 7 * 6. Step 4: Compute the numerator: 9 * 8 * 7 * 6 = 3024. Step 5: Denominator is 4! = 4 * 3 * 2 * 1 = 24. Step 6: Divide 3024 by 24 to get 126. Step 7: Therefore, there are 126 distinct 4 person committees.

Verification / Alternative check:
We can also compute 9C4 using symmetry: 9C4 = 9C5 because choosing 4 members to include is equivalent to choosing 5 members to leave out. Calculating 9C5 = 9! / (5! * 4!) leads to the same result, 126. This symmetry gives a quick cross check that our answer is consistent.

Why Other Options Are Wrong:
120: Close to 5!, but that belongs to a different counting context and not to 9C4. 162 and 170: Both values do not arise from the combination formula with n = 9 and r = 4 and indicate arithmetic or conceptual mistakes. Only 126 fits the correct combination computation.

Common Pitfalls:
A frequent error is to use permutations instead of combinations, for example computing 9P4 instead of 9C4, which overcounts each committee many times due to different orders. Another mistake is failing to simplify the factorial expression correctly, especially when cancelling numerator and denominator factors. Writing the computation step by step and remembering that committee members have no order prevents these issues.

Final Answer:
The number of different 4 person committees that can be formed from 9 people is 126.