L17 | Permutation and Combination 11th | Selection from Identical Objects | JEE Mains & Advanced

L17 | Permutation and Combination 11th | Selection from Identical Objects | JEE Mains & Advanced

This is Lecture 17 in the Permutations & Combinations (P&C) series for JEE Mains & Advanced, focusing on the crucial topic of "Combinations from Identical Objects."

In this detailed lecture, we move beyond basic nCr and explore the methods for selecting items when they are not all distinct. This concept is a favorite in JEE and other competitive exams.

► Key Concepts Covered in this Video:

1. Selections from a Single Group of Identical Objects
Find the number of ways to select 'r' objects from 'n' identical objects
Master the (n+1) formula for selecting at least zero objects from 'n' identical items

2. Rule 2: Selections from Multiple Groups of Identical Objects
Learn the product rule for selecting at least zero items: (a₁+1)(a₂+1)...(aₖ+1)
Understand how to find the number of ways to select at least one item by subtracting the case of zero selections

3. Rule 3: Selections from a Mix of Identical AND Distinct Objects
The complete formula for selections from 'k' identical groups and 'm' distinct items: (a₁+1)(a₂+1)...(aₖ+1) * 2ᵐ
How to find "at least one" selection in these mixed sets

► Practice Problems Solved (including JEE PYQs):

► (0:00) Introduction
► (01:10) Combinations from Identical Objects
► (04:32) Rule 1: Selection of one or r from identical objects
► (05:54) Rule 2: Selecting from 'n' identical objects (n+1 ways)
► (08:15) Rule 3: Selecting from multiple groups of identical objects
Formula for selecting at least zero items: (a₁+1)(a₂+1)...(aₖ+1)
Formula for selecting at least one item: [(a₁+1)(a₂+1)...(aₖ+1)] - 1
► (19:23) Problem 1: Fruit Basket (3 Oranges, 5 Apples, 6 Mangoes)
► (21:05) Problem 2: Red and Black Balls (4 Red, 5 Black)
► (22:03) Problem 3: 'p' copies each of 'n' different books
► (24:22) Problem 4: AIEEE 2012 (10 White, 9 Green, 7 Black Balls)
► (26:11) Problem 5: At least one of each fruit (Identical vs. Different)
► (32:00) Problem 6: The "Set of Teeth" problem (Max population)
► (36:55) Rule 4: Selections from BOTH Identical and Distinct Objects
Formula: (a₁+1)(a₂+1)...(aₖ+1) * 2ᵐ
► (41:39) Problem 7: Letter Selection from "AAAA BB CCC DEF"
► (48:23) Problem 8: JEE Mains 2019 (10 Identical, 21 Distinct)
► (52:31) Problem 9: JEE Mains 2024 (Letters from "MATHEMATICS")
► (58:50) Assignments and next lecture intro

This lecture is essential for building a strong foundation in combinatorics for IIT JEE.








Permutations and Combinations

Combinations from Identical Objects

JEE Mains Maths

JEE Advanced Maths

Combinatorics

JEE Mains 2024

JEE Mains 2019

AIEEE 2012

P&C Class 11

P&C JEE

Selection of Identical Items

Selection of Identical and Distinct Objects

Combinations Formulas

JEE Maths PYQs

IIT JEE Mathematics

Integron Maths

JEE P&C


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