Chapter 1 Counting

Question 1

Fundamental Theorem of Counting

Answer 1

if a job consists of k tasks, the ith of which can be done in ni ways, the entire job can be done in n1n2…*nk ways

Question 2

Counting: ordered, without replacement

Answer 2

n!/(n-r)! n total objects take r at a time

Question 3

Counting: ordered, with replacement

Answer 3

n^r n total objects taken r at a time

Question 4

Counting: unordered, without replacement

Answer 4

n!/(r!(n-r)!) n total objects taken r at a time (n choose r)

Question 5

Counting: unordered, with replacement

Answer 5

(n-1+r)!/(r!(n-1+r)!) n total objects taken r at a time

n-1+r choose r

Question 6

binomial theorem

Answer 6

(X+Y)^N = Sum (n choose k) x^k * y^ n-k

if x+y = 2, this is binomial expansion = 2^n