UNIT 3 BINOMIAL COEFF Flashcards Preview

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Flashcards in UNIT 3 BINOMIAL COEFF Deck (9)
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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