No. of diagonals of polygon=ⁿC₂-n
Permutations No. of ways of arrangement
Ways of selection of r obj. from
n different obj.- ⁿCᵣ= n!/r!(n-r)! Factorial n! = 1.2.3....(n-2)(n-1)(n)
Notations
ⁿCᵣ=ⁿpᵣ/r! ⌊n= n(n-1)(n-2)(n-3)....3.2.1
ⁿCᵣ=ⁿCₙ₋ᵣ 0!=1; 1!=1; 2!=2; 3!=6; 4!=24;
Factorials: 5!=120; 6!=720; 7!=5040;
ⁿCᵣ+ⁿCᵣ₋₁=ⁿ⁺¹Cᵣ Combinations 0-10 8!=40320; 9!=362880;
10!=3628800
If ⁿCₓ=ⁿCᵧ =>n=x+y
Permutations and
n obj. -> n! ways
ⁿCᵣ/ⁿCᵣ₋₁=(n-r+1)/r Combinations Permutation
obj. rep'n
isn't allowed r obj. from n ->
ⁿCᵣ₊₁/ⁿCᵣ=(n-r)/(r+1) when n
ⁿpᵣ= n!/(n-r)!
different
obj. can be n obj. -> nⁿ ways
Out of 'n' obj. 'p' - alike of 1 kind, 'q'- alike of 2nd obj. rep'n
arranged. If
kind 'r'- alike of 3rd kind then permutation= n!/p!q!r! is allowed
r obj. from n -> nʳ ways
Permutations No. of ways of arrangement
Ways of selection of r obj. from
n different obj.- ⁿCᵣ= n!/r!(n-r)! Factorial n! = 1.2.3....(n-2)(n-1)(n)
Notations
ⁿCᵣ=ⁿpᵣ/r! ⌊n= n(n-1)(n-2)(n-3)....3.2.1
ⁿCᵣ=ⁿCₙ₋ᵣ 0!=1; 1!=1; 2!=2; 3!=6; 4!=24;
Factorials: 5!=120; 6!=720; 7!=5040;
ⁿCᵣ+ⁿCᵣ₋₁=ⁿ⁺¹Cᵣ Combinations 0-10 8!=40320; 9!=362880;
10!=3628800
If ⁿCₓ=ⁿCᵧ =>n=x+y
Permutations and
n obj. -> n! ways
ⁿCᵣ/ⁿCᵣ₋₁=(n-r+1)/r Combinations Permutation
obj. rep'n
isn't allowed r obj. from n ->
ⁿCᵣ₊₁/ⁿCᵣ=(n-r)/(r+1) when n
ⁿpᵣ= n!/(n-r)!
different
obj. can be n obj. -> nⁿ ways
Out of 'n' obj. 'p' - alike of 1 kind, 'q'- alike of 2nd obj. rep'n
arranged. If
kind 'r'- alike of 3rd kind then permutation= n!/p!q!r! is allowed
r obj. from n -> nʳ ways
