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Permutation and Combination

Permutation and Combination is an important topic in mathematics that deals with arranging and selecting objects in different ways. It helps students understand how many possible ways a set of items can be arranged or chosen. A Permutation refers to the arrangement of objects where the order matters. For example, arranging students in different positions or forming different numbers from given digits. A Combination refers to the selection of objects where the order does not matter. For example, choosing a group of students from a class.

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Permutations and Combinations Quick Notes
This PDF contains complete and easy revision notes for Permutations and Combinations (MHT-CET Maths). It covers all the important concepts, formulas, and shortcuts required to solve exam questions quickly. Topics covered in this PDF: • Factorial and its properties • Permutation formula 𝑛 𝑃 𝑟 nPr • Permutation of distinct and repeated objects • Circular permutations • Combination formula 𝑛 𝐶 𝑟 nCr • Important identities and properties • Relation between permutation and combination • Quick tips for solving MHT-CET questions These notes are specially designed for fast revision before MHT-CET 2026 and help students understand the difference between arrangement (Permutation) and selection (Combination) clearly.

Formula Bank

Factorial
n!=n(n−1)(n−2)…3×2×1
Permutation (Arrangement)
nPr=\frac{n!}{(n-r)!},n=total\space objects\space r=objects\space selected
Permutation of n Different Objects
Number\space of\space arrangements\space-𝑛!
Permutation with Repetition
If\space objects\space repeat:\frac{𝑛!}{𝑝!𝑞!𝑟!}
Relationship Between Permutation and Combination
nPr​=nCr​×r!

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Assessment 1: MCQ