Mathematics
Mathematics
Problem
A student is to answer 10 out of 13 questions in an examination such that he must choose at least 4 from the first five questions. The number of choices available to him is : (a) 140 (b) 196 (c) 280 (d) 346Intuitive explanation
The key insight is to break this constrained selection into cases based on how many questions you take from the first five. Since you need 10 total and must grab at least 4 from the first five, you're really choosing either 4 or 5 from that group—then filling the rest from the remaining eight questions. Use combinations to count each valid scenario, then add them together.
Intuitive explanation
The key insight is to break this constrained selection into cases based on how many questions you take from the first five. Since you need 10 total and must grab at least 4 from the first five, you're really choosing either 4 or 5 from that group—then filling the rest from the remaining eight questions. Use combinations to count each valid scenario, then add them together.