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?
Aptitude
Permutation and Combination
Difficulty: Easy
Choose an option
Answer
Correct Answer: 1023
Explanation
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