Counting Techniques, Permutation and Combination

Question 1

Suppose there are n₁ ways for E₁ to occur, and n₂ ways for event E₂ to occur we cannot do both E₁ and E₂.

Answer 1

Addition Principle

Question 2

Suppose there are n₁ ways for E₁ to occur, and each possible way that E₁ occurs allows exactly n₂ ways for event E₂ to occur.

Answer 2

Multiplication Principle

Question 3

The number of different ways we can arrange a number of items

Answer 3

Permutations

Question 4

Permutations of n object taking r at a time

Answer 4

nPr = n! / (n-r)!

Question 5

Formula for n!

Answer 5

n! = ( n-1) (n-2) (n-3)…

Question 6

Permutations of Identical objects

Answer 6

P= n! / r₁!* r₂!* r₃!* r₄!*…
or
P = n! / (r1!) (r2!) (r3!) (r4!)…

Question 7

Circular Permutations

Answer 7

P(n) = (n-1)!

Question 8

An arrangement of objects where the order in which the objects are selected does not matter

Answer 8

Combination

Question 9

Selection

Answer 9

Combination

The order or things has NO importance

Question 10

Arrangement

Answer 10

Permutation

The order of things has importance

Question 11

Formula for Combination

Answer 11

nCr = n! / (n-r)! r!