Permutations and Combinations
9 solved problems from JEE previous year papers.
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 specific boys…
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: 7 Boys 3 Girls, Group B: 6 Boys 5 Girls — Picnic Selection
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
Words From KANPUR in Dictionary Order: 440th Word
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…