UNIT 3 BINOMIAL COEFF Flashcards
1
Q
Two kinds of proofs
A
combinatorial: set into subsets, no. of ways to select
algebraic: manip of factorials
2
Q
binom coeff
A
of form nCr
3
Q
Binomial expression
A
two terms add/sub
4
Q
binomial theorem
A
pic 11111
5
Q
nCr ?
A
n!/(n-r)!r!
6
Q
pascal triangle
A
0C0 1C0 1C1 2C0 2C1 2c2..
7
Q
multinomial theorem
A
n!/exp!exp!…
no of terms = C(n+t-1, n)
t = letters
8
Q
princi of in/ex
A
sum rule -> union disjoint not disjoint union -> in/ex / sieve proof2 |A U B| = |A| + |B\ - \AintB| not -> uni -
9
Q
pigeon hole princi
A
m pigeons n pigeon holes
at least 1 pigeon hole with 2 pigeons
(m-1/n)+1 pigeons
proof
