Combinatorics and Counting

Question 1

What is the fundamental principle of counting?

Answer 1

If an event can occur in n1 ways, and a second event in n2 ways, and a third in n3 ways, … and an i-th event in ni different ways, then the total number of ways the sequence 1 to i can occur is i! (i factorial)

Question 2

In how many was can N objects be chosen from a set of N distinct objects where the order is important?

Answer 2

NpN ( = N!)

Question 3

In how many ways can k objects from a set of N distinct objects be chosen, where k < N?

Answer 3

NPK

Question 4

What is the formula of NpK?

Answer 4

N!

(N-k)!

Question 5

How do you calculate the number of permutations of N objects when n1 are alike in one respect, n2 are alike in a second respect, …, and ni are alike in an i-th respect

Answer 5

N!

n1! x n2! x … x ni!

Question 6

How do we choose k objects from N if order is unimportant?

Answer 6

NCK

Question 7

How many ways can k objects be chosen from a set of N when objects are replaced?

Answer 7

N^k

Question 8

What is the formula for NCK?

Answer 8

N! / (N-k)!k!