Permutations and Combinations

13 solved problems from JEE previous year papers.

Permutations and Combinations

The Number of Triangles Whose Vertices Are at the Vertices of a Regular Octagon but None of Whose Sides Is a Side of the Octagon Is

JEE Main 2024 PYQ: find the number of triangles whose vertices are vertices of a regular octagon, but none of whose sides…
AIEEE 2008

How Many Different Words Can Be Formed by Jumbling the Letters of the Word MISSISSIPPI in Which No Two S’s Are Adjacent

AIEEE PYQ: find how many distinct arrangements of the letters of MISSISSIPPI have no two S’s adjacent, using the gap method…
Permutations and Combinations

The Number of Six-Digit Numbers That Can Be Formed Using the Digits 1, 3, 5, 7, 9 Such That Each Digit Is Used at Least Once Is

Find how many six-digit numbers can be formed from the digits 1,3,5,7,9 with each digit used at least once, by choosing which…
Permutations and Combinations

How Many Words Can Be Formed From the Letters of the Word DAUGHTER Such That All Vowels Are Not Together

Find how many words can be formed from the letters of DAUGHTER such that all the vowels are not together, by subtracting the…
Permutations and Combinations

Integers Between 100 and 1000 With Digit Sum Equal to 14

Count the 3-digit integers between 100 and 1000 whose digits sum to 14, using stars-and-bars with inclusion-exclusion for the…
Permutations and Combinations

3 Girls and 4 Boys in a Queue, B1 and B2 Not Adjacent to Each Other

In a group of 3 girls and 4 boys, there are two boys B1 and B2. The number of ways they can stand in a queue with girls together,…
Permutations and Combinations

Seven Digit Numbers With Digit Sum 11, Using Only 1, 2 and 3

Let P be the set of seven digit numbers with sum of their digits equal to 11, formed using only digits 1, 2 and 3. Find the…
Permutations and Combinations

5 Letters Chosen From Alphabet, Arranged in Order, Middle Letter M

A JEE Main 2025 problem where fixing alphabetical order turns an arrangement question into a pure selection (combinations)…
Permutations and Combinations

4 Boys, 3 Girls Seated: Girls Together, B1 and B2 Not Adjacent

A JEE Main 2025 seating-arrangement problem solved with the block method for ‘girls together’, then placing two…
Permutations

5-Digit Numbers >50000, Digits 0-7, First+Last Digit ≤8

How many 5-digit numbers above 50,000, built from digits 0-7 with repetition, have first-plus-last digit at most 8? JEE Main…
Permutations and Combinations

Group A Consists of 7 Boys and 3 Girls, Group B Consists of 6 Boys and 5 Girls. The Number of Ways 4 Boys and 4 Girls Can Be Invited for a Picnic if 5 of Them Must Be From Group A and the Remaining 3 From Group B

A JEE Main 2025 combinatorics problem: invite 4 boys and 4 girls for a picnic with 5 from one group and 3 from another. Solved…
Permutations

If All the Words, With or Without Meaning, Made Using All the Letters of the Word KANPUR Are Arranged as in a Dictionary, Then the Word at the 440th Position Is

All arrangements of the letters of KANPUR are sorted like a dictionary. Which word sits at position 440? A JEE Main 2025…
Permutations

6-Letter Words From MATHS Where Every Letter Appears Twice

How many 6-letter words can be formed from MATHS if every letter used must appear at least twice? A JEE Main 2025 permutations…