Basic Formulas of Permutations and Combinations
The following are the formulas relevant to Permutations and Combinations questions:
| S.No | To Calculate | Formulas |
|---|---|---|
1 |
Permutation formula |
nPr = (n!) / (n-r)! |
2 |
Combination formula |
nCr = nC(n-r) = n! / {r! (n-r)!} |
3 |
Relation between permutation and combination |
nPr = nCr * r ! |
4 |
Permutation when repetition is allowed |
nPr = n^r |
5 |
Combination when repetition is allowed |
nCr =( n+r-1)! / {r! (n-r)!} |
6 |
Number of permutations of n distinct things taking them all at a time |
nPn = n! |
7 |
Number of circular permutations (arrangements) of n distinct things |
(n-1)! |
8 |
Number of circular permutations (arrangements) of n distinct things, when clockwise and anticlockwise arrangements are not different (i.e.,one is the mirror image / inverted image of the other) |
(n-1)!/ 2 |
9 |
Number of ways in which one or more objects can be selected from n distinct objects (i.e., we can select 1 or 2 or 3 or … or n objects at a time) |
nC1 + nC2 + ... + nCn = (2^n) - 1 |
10 |
Number of ways in which one or more objects can be selected out of S1 alike objects of one kind, S2 alike objects of second kind , S3 alike objects of third kind and so on ... Sn alike objects of nth kind |
(S1 + 1) (S2 + 1)(S3 + 1)...(Sn + 1) - 1 |
11 |
If there are n persons present in a party and every person shakes hands with every other person. Then |
Total number of handshakes = nC2 |
12 |
Number of triangles that can be formed by joining the vertices of a polygon of n sides |
nC3 |
13 |
Number of quadrilaterals that can be formed by joining the vertices of a polygon of n sides |
nC4 |
14 |
Suppose there are n points in a plane out of which m points are collinear. Number of triangles that can be formed by joining these n points as vertices |
nC3 - mC3 |
15 |
Suppose there are n points in a plane out of which no three points are collinear. Number of triangles that can be formed by joining these n points |
nC3 |
16 |
Suppose there are n points in a plane out of which m points are collinear. Number of straight lines that can be formed by joining these n points |
nC2 - mC2 + 1 |
17 |
Suppose there are n points in a plane out of which no points are collinear. Number of straight lines that can be formed by joining these n points |
nC2 |
18 |
Number of rectangles that can be formed by using m horizontal lines and n vertical lines |
mC2 × nC2 |
19 |
Number of diagonals that can be formed by joining the vertices of a polygon of n sides |
n(n-3)/2 |
Quick Tip: Do you know? You can learn Permutations and Combinations formulas quickly if you first understand the fundamental concepts of Permutations and Combinations.
FAQsFAQs
How do you benefit from learning Permutations and Combinations formulas?
One of the significant benefits of understanding Permutations and Combinations formulas is the capability to quickly and accurately address simple formula-based questions.
How to remember Permutations and Combinations formulas for a longer time?
Following are the techniques you can use to memorise Permutations and Combinations formulas:
For a start, you can start understanding theconcepts of the Permutations and Combinations. It will help you find out why a formula is used.
Keep a separate piece of paper and write down each formula on the Permutations and Combinations topic you need to memorise.
Write down and examine each Permutations and Combinations formula, but this time with intervals. Write the equation, then take a 2-minute break to think about it before writing it again.
Your memory is more likely to associate with the formula you want to remember if you use it more often. Solve the problems employing the formula.
Visualise and repeat out loud the formula occasionally. Create Permutations and Combinations formulas flashcards to help with this. You can also use these flashcards while practicing the Permutations and Combinations questions.
The formula should be written down and posted somewhere you will see daily. They'll be subconsciously imprinted into your memory.
How conceptual understanding of Permutations and Combinations topic helps in remembering its formulas?
Conceptual understanding will help you to make sense of the Permutations and Combinations formulas. Conceptual understanding is concentrated on describing why things happen as opposed to how to make them happen. They help you understand the true motive for employing the Permutations and Combinations formulas.
