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 digit-range constraints.
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Sum of nCr/(r+1) From r=0 to n
A step-by-step derivation of the summation of nCr/(r+1) from r=0 to n, using the identity that turns each term into a binomial coefficient one order up.
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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, boys together, but B1, B2 not adjacent.
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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 number of elements in P.
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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) problem, split around a fixed middle letter.
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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 into non-adjacent gaps.
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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 case by case.