L15 | P & C | Restricted Combinations Part 2 | Most Important Questions For JEE Mains & Advanced |

Hello Future IITians/NITians! 🙏

Welcome back to Integron Maths! This is Lecture 15 in our Permutations and Combinations series, focusing on the most important and frequently asked questions on Restricted Combinations for JEE Mains & Advanced.

In this session, we dive deep into complex combination problems where specific conditions and restrictions apply. Mastering these concepts is crucial for scoring high in the P&C section of the JEE exam. We'll be solving a variety of challenging problems, including several Previous Year Questions (PYQs) from JEE Mains and Advanced.

Q.No. 7 (Horse Selection): A great problem to master the Principle of Inclusion-Exclusion, where you select from a special group while excluding specific pairs that cannot be together.
Q.No. 8 (Party Planning): This question is a classic application of finding the maximum value of $^nC_r$, which occurs when the number of items to be chosen is $n/2$.
Q.No. 9 (Team Fights): A unique problem that combines Combinations with Quadratic Equations. You'll learn how to set up an equation and find the maximum value to solve the problem.
Q.No. 10 (JEE Mains - Cricket Team): Tackle a realistic team selection scenario with multiple "at least" conditions and pre-selected players (captain/vice-captain), requiring careful case analysis.
Q.No. 11 (JEE Mains - Boys & Girls Group): A perfect example of the "never together" restriction. The solution involves subtracting the unwanted cases from the total possible selections.
Q.No. 12 (JEE Mains - Couple's Party): This problem tests your ability to handle selections from two completely separate pools of people while satisfying conditions for the final group.
Q.No. 13 (JEE Mains - Badminton Tournament): Learn how to work backward. Here, the number of matches is given, and you need to use combination logic to find the initial number of players.
Q.No. 14 (JEE Mains - Boys Refusing Team): A straightforward and important application of the "never together" principle within a mixed-team formation problem.
Q.No. 15 (JEE Advanced - Student Teams): A challenging question on dividing distinct items into groups of unequal sizes, with added restrictions on where specific students can be placed.
Q.No. 16 (JEE Advanced - Committee Formation): A comprehensive, multi-part question that's a complete workout for restricted combinations, covering everything from "at least" conditions to "not together" rules in one problem.



Maximization Problems: Using combinations to set up a function and find the maximum possible outcomes.



JEE Mains & Advanced PYQs: Detailed solutions to questions from past JEE papers to give you a real-exam feel.



⏰ Timestamps:



00:00 - Introduction of Restricted Combination
02:49 - Problem 7: Advanced Problem on Horse Selection with Multiple Conditions
12:30 - Problem 8: Maximizing the Number of Parties
23:31 - Problem 9: Maximizing Fights Between Teams (Application of Maxima-Minima)
37:10 - Problem 10 (JEE Mains): Cricket Team Selection (Batsmen/Bowlers)
41:50 - Problem 11 (JEE Mains): Group Formation (Boys/Girls, Not Together)
47:43 - Problem 12 (JEE Mains): Party Invitation by a Couple
54:32 - Problem 13 (JEE Mains): Mixed Doubles Tournament
1:01:15 - Problem 14 (JEE Mains): Team Formation with Boys Refusing to be Together
1:03:46 - Problem 15 (JEE Advanced): Dividing Students into Teams with Restrictions
1:09:38 - Problem 16 (JEE Advanced): Multi-Concept Matching List Question
1:27:10 - Conclusion and Summary

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Primary Keywords:

Restricted Combinations

Permutations and Combinations JEE

P&C Important Questions

JEE Mains & Advanced PYQs

Secondary Keywords:

Combination with conditions

Conditional selection problems

"Never together" combination problems

"All or none" combination problems

Committee formation questions

JEE Maths lecture

P&C tricks for JEE

JEE Advanced previous year questions Maths

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