Find the number of distinct 4-element subsets that can be formed from the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}.

Introduction / Context:
This problem is a straightforward application of combinations. We are asked to count how many different subsets of size 4 can be chosen from a fixed set of 11 distinct elements. Order inside a subset does not matter, which means we are not forming arrangements or permutations, but pure combinations. Such questions reinforce the idea of choosing items without regard to order, which is central to many counting problems in aptitude tests and mathematics competitions.

Given Data / Assumptions:
- Underlying set: {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}.
- Total number of elements in the set: 11.
- We must form subsets that contain exactly 4 elements.
- The order of elements in a subset does not matter.
- Each element can either be included or excluded, but cannot be repeated.

Concept / Approach:
When we choose r elements from a set of n distinct elements without caring about order, we use the combination formula nCr. Here, n = 11 and r = 4. The formula is:
nCr = n! / (r! * (n - r)!).We substitute n = 11 and r = 4 into this formula and simplify carefully. The result gives the total number of different 4-element subsets that can be formed.

Step-by-Step Solution:
Step 1: Identify n and r: n = 11, r = 4.Step 2: Use the formula 11C4 = 11! / (4! * 7!).Step 3: Rewrite 11! / 7! as 11 * 10 * 9 * 8, because 7! cancels from numerator and denominator.Step 4: So 11C4 = (11 * 10 * 9 * 8) / (4 * 3 * 2 * 1).Step 5: Compute the numerator: 11 * 10 = 110; 9 * 8 = 72; 110 * 72 = 7920.Step 6: Compute the denominator: 4 * 3 * 2 * 1 = 24.Step 7: Divide: 7920 / 24 = 330.

Verification / Alternative check:
You can check the result using a symmetry property: 11C4 is equal to 11C7, because choosing 4 elements to include is equivalent to choosing 7 elements to exclude. Many standard combination tables or calculators confirm that 11C4 = 330. Also, if you roughly estimate, 10C4 = 210 and 12C4 = 495, so a value between 210 and 495 is reasonable, and 330 fits nicely in this range.

Why Other Options Are Wrong:
- 340 and 370 are close but arise from arithmetic mistakes, such as mis-multiplying or mis-dividing when simplifying 11C4.
- 320 is also a common slip when performing the division 7920 / 24 too quickly or truncating wrongly.

Common Pitfalls:
Common errors include confusing combinations with permutations and using 11P4 instead of 11C4, which would count ordered selections and give a much larger number. Another typical mistake is to expand the factorials incorrectly or not cancel common factors properly, leading to minor arithmetic errors. Writing out the product explicitly and cancelling factors step by step helps avoid such problems.

Final Answer:
The number of 4-element subsets that can be formed from the set {1, 2, ..., 11} is 330.