From a committee of 17 people, in how many different ways can you select a subcommittee of 7 members if only the selection matters and the order of members does not matter?

Introduction / Context:
This problem is a direct application of combinations in combinatorics. We are forming a smaller subcommittee from a larger committee, and only the set of people in the subcommittee matters. Their seating order or any ranking is not relevant at this stage. Such selection problems are extremely common in aptitude tests, management entrance exams, and interview questions that test logical thinking and basic mathematics.

Given Data / Assumptions:

• Total number of people on the main committee: 17.
• Number of people required in the subcommittee: 7.
• All 17 people are distinct individuals.
• The order in which the 7 people are chosen does not matter.
• No person can be chosen more than once.

Concept / Approach:
When we select r people from n distinct people and we only care about which people are chosen (not the order), we use combinations. The formula is:
nCr = n! / (r! * (n - r)!) Here, n = 17 and r = 7. We simply compute 17C7 using this formula. This gives the number of unique 7-member groups that can be formed from the 17 members.

Step-by-Step Solution:
Step 1: Identify n = 17 and r = 7. Step 2: Use the combination formula 17C7 = 17! / (7! * 10!). Step 3: Write 17! / 10! as 17 * 16 * 15 * 14 * 13 * 12 * 11. Step 4: Compute numerator: 17 * 16 * 15 * 14 * 13 * 12 * 11. Step 5: Divide this product by 7! = 7 * 6 * 5 * 4 * 3 * 2 * 1. Step 6: Carefully cancel common factors and simplify step by step to avoid mistakes. Step 7: After simplification, we get 17C7 = 19448.

Verification / Alternative check:
We can verify the answer by using the symmetry property of combinations. Note that 17C7 = 17C10 because choosing 7 members to include is equivalent to choosing 10 members to exclude. Many scientific calculators can compute 17C7 directly and confirm the result 19448. Checking with any reliable combinatorics table or tool also matches this value, which increases confidence in the result.

Why Other Options Are Wrong:
19000: A rounded-looking number but not the result of 17C7. 19821: Numerically close but does not match the exact combination formula result. 19340: Another nearby value that likely arises from an arithmetic error in cancellation. Only 19448 satisfies the exact combination computation for 17C7.

Common Pitfalls:
Students often confuse combinations with permutations and may wrongly compute 17P7. That would be much larger and completely wrong here. Another common error is incorrect simplification of factorials due to skipping steps or doing mental arithmetic too quickly. Writing out cancellation clearly and using the combination formula carefully helps avoid these mistakes. It is also important not to treat 17C7 as 17^7, which is a completely different operation.

Final Answer:
The number of different 7-member subcommittees that can be selected from a committee of 17 people is 19448.