Quant · Modern Maths

Permutations and Combinations

6 sub-topics · 62 lessons · 75 questions · 28 PYQs

Videos are being made — every lesson's notes and practice are ready now.

Counting Numbers and Words10 lessons · 11 questions · 4 PYQs

Arrangements12 lessons · 12 questions · 4 PYQs

Selections12 lessons · 19 questions · 6 PYQs

Distribution and Partitions11 lessons · 11 questions · 5 PYQs

Counting in Geometry and Grids11 lessons · 12 questions · 5 PYQs

Tournaments and Handshakes6 lessons · 10 questions · 4 PYQs

Formula sheet

Climbing stairs one or two at a time
$f(n)=f(n-1)+f(n-2)$
Selections with identical items
$(p+1)(q+1)\,2^{d}-1$
Arrangements with repeated letters
$\dfrac{n!}{p!\,q!\,r!}$
Permutations from combinations
${}^{n}P_{r}=r!\binom{n}{r}$
Number of subsets
$\sum_{r=0}^{n}\binom{n}{r}=2^{n}$
Solutions of an inequality
$x+y+z\le n,\ x,y,z\ge0:\ \binom{n+3}{3}$
Arrangements of r out of n distinct digits
${}^{n}P_{r}=\dfrac{n!}{(n-r)!}=n(n-1)\cdots(n-r+1)$
Combinations and their symmetry
$\binom{n}{r}=\dfrac{n!}{r!\,(n-r)!}=\binom{n}{n-r}$