P&C Formula Capsule 8 | Division, Distribution & Beggar's Method | Short Notes | JEE, NDA, CUCET

Welcome to Formula Capsule No. 8! One of the most confusing topics in Combinatorics is distinguishing between Dividing into Groups vs Distributing to People. Shubham Sir breaks down the "Equal Groups" trap and the "Beggar's Method" for identical objects.

🚀 Formula Cheat Sheet (Covered in this Video):

1. Division into Groups (Distinct Objects):

Unequal Groups: To divide (m+n) things into groups of m and n: Formula: (m+n)! / (m! * n!)

Equal Groups: To divide 2n things into two equal groups of n: Formula: (2n)! / (n! * n! * 2!) Note: We divide by k! (here 2!) to remove order between identical groups.


2. Distribution to Persons:

Rule: First Group, Then Distribute.


Total Ways = (Division Ways) * r!

Direct Formula (Distinct Things): Distributing n distinct things to p persons (any number to anyone): p^n

3. Distribution of Identical Things (Beggar's Method):

Non-Negative Solutions (Zero allowed): Equation: x1 + x2 + ... + xp = n Formula: (n + p - 1) C (p - 1)


Positive Integral Solutions (At least 1): Formula: (n - 1) C (p - 1)


Broad Topics:
Permutations and Combinations, Combinatorics
P&C JEE Mains, Counting Principles, Selection and Arrangement.

Exam Focus: JEE Mains 2026
JEE Advanced Maths
IIT JEE Preparation
NDA Maths
MHCET
WBJEE
BITSAT
CUCET.

Content Type: Maths
Short Tricks
Formula Revision
JEE Maths PYQ
Problem Solving Techniques
One Shot Revision.

Key Concepts:
nCr and nPr
Inclusion Exclusion Principle
Division and Distribution
Geometrical Problems,
Number Theory in P&C
Beggar's Method
Derangement
Rank of Word.

Branding:
Integron Maths
Shubham Sir
Best Maths Teacher for JEE.

Target Exams:

Engineering: JEE Mains, JEE Advanced, BITSAT, WBJEE, MHCET, VITEEE.

Defense: NDA, CDS.

University: CUCET (CUET), ISI.

🔑 Tags: #DivisionAndDistribution #BeggarsMethod #JEEMaths #Combinatorics #IdenticalObjects #IntegronMaths #ShubhamSir #IITJEE #NDAExam #MHCET #CUCETPreparation #StarsAndBars