Courses
Courses for Kids
Free study material
Offline Centres
More
Store Icon
Store
seo-qna
SearchIcon
banner

How does nPr and nCr work?

Answer
VerifiedVerified
435.3k+ views
1 likes
like imagedislike image
Hint: Permutation and Combinations, the various ways in which objects from a set may be selected, generally without replacement to form subsets. The selection of subsets is called a permutation when the order of selection is a factor. A combination is not a factor.

Complete step-by-step solution:
nPr and nCr are the probability function that represents permutation and combinations. The formula of finding nPr and nCr is
nPr=n!(nr)!
nCr=n!r!(nr)!
Here n is the total number of objects and r is the number of selected objects.
Generally nPr is used for permutation, representing selecting a group of ‘r’ objects from a group of ‘n’ number of objects. The order of objects matters in case of permutation. The formula of permutation is:
nPr=n!(nr)!
For example 7 books have to arrange 5 on the shelf. So we can solve it from permutation.
7P5=7!(75)!
7P5=7!2!
7P5=7×6×5×4×3×2×12×1
7P5=2520ways
And nCr is used for combinations representing selecting of objects from a group of objects where order of object does not matter.
nCr=n!r!(nr)!
For example 7 books have to arrange 5 on the shelf. So we can solve it by combination.
7C5=7!5!(75)!
7C5=7!5!×2!
7C5=7×6×5×4×3×2×15×4×3×2×1×2×1
7C5=21

Note: Factorial is a function that multiplies a number by every number below it. The function is used, among other things, to find the number of ways ‘n’ objects can be arranged. Factorial may be indicated by ‘!’ by this sign. Factorial is used for non-negative real numbers. For a negative number it will be a complex number.
Latest Vedantu courses for you
Grade 10 | MAHARASHTRABOARD | SCHOOL | English
Vedantu 10 Maharashtra Pro Lite (2025-26)
calendar iconAcademic year 2025-26
language iconENGLISH
book iconUnlimited access till final school exam
tick
School Full course for MAHARASHTRABOARD students
PhysicsPhysics
BiologyBiology
ChemistryChemistry
MathsMaths
₹36,600 (9% Off)
₹33,300 per year
Select and buy