Selection with Mandatory Constraint
Selection with Mandatory Constraint problems involve selecting a committee or team where certain specific individuals must be included (or must be excluded). These problems simplify by fixing the mandatory selections first, then selecting the remaining from the available pool.
What You'll Learn
Introduction to Selection with Mandatory Constraint
Selection with Mandatory Constraint problems involve selecting a committee or team where certain specific individuals must be included (or must be excluded). These problems simplify by fixing the mandatory selections first, then selecting the remaining from the available pool.
Prerequisites
How to Solve Selection with Mandatory Constraint Problems
Step 1: Identify the number of mandatory inclusions (must be in committee)
Step 2: Subtract mandatory inclusions from total committee size to get remaining slots
Step 3: Subtract mandatory inclusions from total pool to get available pool
Step 4: Select remaining slots from available pool using combination formula
Step 5: For mandatory exclusions, simply remove those people from the pool entirely
Step 6: For 'at least one' conditions, use complementary counting
Step 7: Verify that mandatory selections don't exceed committee size
Example Problem
Example: From 10 people, a committee of 5 is to be formed. If 2 specific people must be included, how many ways? Solution: Step 1: Mandatory inclusions: 2 people Step 2: Remaining slots: 5 - 2 = 3 Step 3: Remaining pool: 10 - 2 = 8 people Step 4: Select 3 from 8: ⁸C₃ = 56 Answer: 56 ways
Pro Tips & Tricks
- Must include: reduce both committee size and pool size by the number of mandatory members
- Must not include: reduce pool size only
- For 'at least one' from a group: total selections - selections with none from that group
- For 'exactly k' from a group: select k from that group, rest from others
- When both inclusion and exclusion conditions exist, handle inclusion first
- If mandatory members are from different groups, treat them as already selected
Shortcut Methods to Solve Faster
Common Mistakes to Avoid
Practice Worksheets
Practice makes perfect! Work through these worksheets to master Selection with Mandatory Constraint. Each worksheet contains 20 questions with detailed explanations. Start from Worksheet 1 and progress through increasing difficulty levels.
Exam Importance
Selection with Mandatory Constraint is an important topic for various competitive exams. Here's how frequently it appears:
Ready to Master Selection with Mandatory Constraint?
Start with Worksheet 1 and work your way up to expert level! Each worksheet includes: