Permutations and Combination — Class 11 Maharashtra HSC Mathematics revision notes
A 4-page visual revision sheet for Permutations and Combination, written for Class 11 Maharashtra HSC Mathematics. Formulas, diagrams and the traps that cost marks, laid out to be read the night before rather than the term before. Free, and it opens inside CapCompass.
Page 1 as PDF
Permutations and Combination in one look
order matters for a permutation, order is thrown away for a combination
Two fundamental principles of counting
- addition principle: SEPARATE operations in m or n ways, no overlap: EITHER one is m+n ways
- multiplication principle: one operation in m ways, then another in n ways: BOTH is m× n ways
- 'OR' signals addition; 'AND' or 'followed by' signals multiplication
- invariance principle: the count never depends on the order the choices are made or listed
Factorial notation
- definition, n a positive integer
n! = n×(n-1)×(n-2)×…×2×1 - by convention
0! = 1
Addition then multiplication together
Q. how many even numbers, formed from the digits 2,3,7,8, are less than 1000?
- 1-digit even numbers: only 2 or 8 qualify, 2 ways
- 2-digit even numbers: unit's place even (2 ways), ten's place any of 4 digits: 4×2=8 ways
- 3-digit even numbers: unit's place even (2), ten's and hundred's place any (4 each): 4×4×2=32 ways
Answer: 2+8+32=42
Page 1 of 4. The full sheet, all 4 pages, opens free in the app.
What this Permutations and Combination sheet covers
- Two fundamental principles of counting
- Factorial notation
- definition, n a positive integer
- by convention
- Addition then multiplication together
- Permutations of distinct objects
- arranging n distinct objects, r at a time, r≤ n
- all n objects at once, r=n
- Arranging letters of a word
- Properties of nPr
- All at once
- None chosen
- One chosen
- Peel off one
- Solving for n in an nPr equation
- Permutations with some objects identical
- n objects, n_1 of one kind, n_2 of a second, ..., n_k of a kth kind
- Arrangements with repeated letters
- Circular permutations
- n distinct objects, direction matters
- clockwise and anticlockwise treated as the same
- n objects with m alike
- Circular permutation with a pair together
- Combinations
- selecting r objects from n, order ignored
- link to permutations
- Properties of nCr
- Symmetry
- Full or none
- Pascal's rule
- All subsets
- Direct evaluation of nCr
- Finding n and r from a ratio
- Choosing to arrange, or just choosing
- Permutation
- Combination
- Traps that cost marks
- Tricks that save time
How CapCompass uses this sheet
These notes are not a standalone PDF. CapCompass plans Mathematics chapter by chapter against your real exam dates and free hours, and when the plan reaches Permutations and Combination the sheet opens inside the study block itself — at the page covering the sub-topic that block is on, with the timer still running. Revision arrives at the moment the plan says revise, instead of having to be gone looking for.