Permutations and Combinations · Question 3

JEE Advanced 2024 Paper 1NumericalMedium📈 Topic in 33% papers+4

A group of 9 students, s1,s2, ,s9, is to be divided to form three teams X,Y, and Z of sizes 2,3, and 4, respectively. Suppose that s1 cannot be selected for the team X, and s2 cannot be selected for the team Y. Then the number of ways to form such teams, is .

Answer

665

Solution

Use inclusion–exclusion.

Total = 9!2! 3! 4!=1260

s1 X: 81 73=280

s2 Y: 82 62=28 15=420

Both: 71 62=105

Required =1260-280-420+105=665

Answer: 665

JEE Advanced 2024 Paper 1

Keep practising — Permutations and Combinations

The number of ways to distribute 10 identical red pens and 14 identical blue pens among four persons such that each person gets 6 pens, is .

JEE Advanced 2026 Paper 1

Let S be the set of all seven-digit numbers that can be formed using the digits 0, 1 and 2. For example, 2210222 is in S, but 0210222 is NOT in S. Then the number of elements x in S such that at least one of the digits 0 and 1 appears exactly twice in x, is equal to .

JEE Advanced 2025 Paper 1

All Permutations and Combinations PYQs →

PDFDownload Permutations and Combinations PYQs as PDF Free, with answer key and a QR code to every solution — print it or study offline⬇

All JEE Advanced Mathematics chapters

Class 11Relations and Functions Trigonometric Functions Complex Numbers and Quadratic Equations Permutations and Combinations Binomial Theorem Sequences and Series Conic Sections Limits and Derivatives Statistics

Class 12Relations and Functions (Class 12)Inverse Trigonometric Functions Matrices Determinants Continuity and Differentiability Application of Derivatives Integrals Application of Integrals Differential Equations Vector Algebra Three Dimensional Geometry Probability (Class 12)