Permutations & Combinations | 10 Most Important Problems | Selection + Arrangement | JEE | ( L22 )

In this Permutations and Combinations lecture (L-22), we master the critical concepts of Selection and Arrangement and the Gap Method for JEE Mains and Advanced 2026. If you are struggling with "boys and girls standing in a row" problems or complex word formation questions like 'INVOLUTE' and 'DISTRIBUTION', this One Shot style lecture covers every variation you need to know.

We break down high-weightage JEE topics including restricted permutations, relative ordering of speakers, and identical object selection. This video is perfect for Class 11 students and JEE aspirants aiming to boost their P&C scores.

🚀 IN THIS LECTURE YOU WILL LEARN:

Selection vs. Arrangement: How to handle vowels and consonants together (Word: INVOLUTE).

The Gap Method: Solving "no two sit together" problems (Boys & Girls Arrangement).

Restricted Permutations: Handling specific constraints (e.g., B1 and B2 never adjacent).

Dictionary & Grouping Problems: Forming numbers and words from identical/distinct objects.

JEE Advanced Level Problem Solving: Step-by-step solutions for non-consecutive visit problems.

Problems Discussed :-

Q1: How many words, with or without meaning, consisting of 3 vowels and 2 consonants can be formed from the letters of the word INVOLUTE?

Q2 (JEE Mains 2025): In a group of 3 girls and 4 boys, there are two boys B1 and B2. The number of ways in which they can stand in a queue such that all girls stand together, all boys stand together, but B1 and B2 are not adjacent to each other is?

Q3: Find the number of different seven-digit numbers that can be written using only three digits 1, 2 & 3 under the condition that the digit 2 occurs exactly twice in each number.

Q4: In how many ways can 6 boys & 6 girls stand in a row so that:(i) Girls & boys sit alternately.(ii) No girls sit together.(iii) No boys sit together.

Q5: 12 boys and 2 girls are to be seated in a row such that there are at least 3 boys between the 2 girls. The number of ways this can be done is

Q6 (JEE Advanced 2020): An engineer is required to visit a factory for exactly four days during the first 15 days of every month, and it is mandatory that no two visits take place on consecutive days. Then the number of all possible ways in which such visits can be made during 1-15 June 2021 is?

Q7: In how many ways can we select 3 letters from the word PROPORTION?

Q8: Find the number of ways to select:(i) 5 fruits(ii) 4 fruitsfrom 5 identical apples, 4 bananas, 4 oranges, and 3 distinct fruits.

Q9: The total number of words (with or without meaning) that can be formed out of the letters of the word DISTRIBUTION taken four at a time is?

Q10: In a conference, 10 speakers are present. If S1 wants to speak before S2, and S2 wants to speak after S3, then the number of ways all 10 speakers can give their speeches with the above restriction is? 26


🕒 TIMESTAMPS & QUESTION BANK:

00:00 - Introduction to Selection & Arrangement

00:48 - Q1: Word Formation (INVOLUTE): Words with 3 vowels & 2 consonants.

04:00 - Q2: Queue Arrangement (JEE Mains 2025): 3 Girls, 4 Boys (B1 & B2 separated).

10:43 - Q3: Number Theory: 7-digit numbers using {1,2,3} with '2' appearing twice.

14:04 - Q4: The Gap Method: 6 Boys & 6 Girls (Alternate seating/No two together).

20:58 - Q5: Linear Arrangement: 12 Boys & 2 Girls with at least 3 boys between them.

28:49 - Q6: JEE Advanced 2020: Engineer visits on non-consecutive days.

37:04 - Q7: Selection Strategy: Choosing 3 letters from 'PROPORTION'.

42:46 - Q8: Fruit Selection: Picking 5 or 4 fruits from Identical vs. Distinct sets.

53:48 - Q9: Word Formation: Words from 'DISTRIBUTION' taken 4 at a time.

59:00 - Q10: Relative Ordering: 10 Speakers with specific speaking order constraints.

1:01:00 - next lecture

📚 RELATED TOPICS:

Permutations and Combinations Class 11

JEE Maths One Shot P&C

Gap Method Permutation

Arrangement of Identical Objects

Rank of a Word in Dictionary
Permutations and Combinations JEE Mains
Selection and Arrangement P&C
Gap Method Permutation and Combination
Permutation and Combination JEE Advanced Questions
Arrangement of Boys and Girls in a Row, Number Formation Problems P&C Dictionary Rank Problems JEE
Selection from Identical Objects
Restricted Permutations JEE,
JEE Maths Permutations and Combinations One Shot
Integron Maths P&C
P&C Lecture 22
How to solve P&C problems JEE
Circular Permutation vs Linear Permutation
Arrangement with Constraints JEE

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