A student attempts a set of 10 questions and may solve any subset, provided at least one question is attempted. In how many ways can the student choose which questions to solve?

Introduction / Context:Each question can be solved or not solved, leading to a subset selection model. We exclude the empty subset because at least one question must be attempted.

Given Data / Assumptions:

• Total questions = 10.
• Any subset allowed except the empty subset.

Concept / Approach:The number of all subsets of a 10-element set is 2^10. Excluding the empty set leaves 2^10 − 1.

Step-by-Step Solution:2^10 = 1024.Nonempty subsets = 1024 − 1 = 1023.

Verification / Alternative check:Sum over k from 1 to 10 of C(10,k) equals 2^10 − 1 by the binomial theorem.

Why Other Options Are Wrong:1024 includes the empty subset; 1025 is impossible; 1000 is unrelated.

Common Pitfalls:Forgetting to remove the empty selection when “at least one” is required.

Final Answer:1023