A conference schedule allows attendees to select 1 morning workshop out of 6 options, 1 keynote session out of 3 options, and 1 afternoon panel out of 4 options. However, 2 specific morning workshops conflict with 1 specific afternoon panel and cannot be chosen together. How many different valid 3-session schedule combinations can an attendee create?
Answer: 66 combinations
Answer
An attendee can create 66 different valid 3-session schedule combinations.
According to the Fundamental Counting Principle, the total unrestricted number of schedule combinations is . The restriction specifies that 2 morning workshops cannot be paired with 1 specific afternoon panel. Since there are 3 keynote speaker options available for any schedule, the number of invalid combinations is . Subtracting the invalid options from the total gives valid schedule combinations.
Step-by-Step Solution
Key Concept
Fundamental Counting Principle with Restrictions
Estimated Time:1m 30s