Definition

Random Experiment

Example

Definition

Sample Space

Definition

Event

Example

Solution

Definition

Mutually Exclusive Events

Example 1

Four law students have to decide if they should return to the scene of a crime in order to retrieve the body of man they had just murdered. They agree to toss a coin, and if it lands on heads, then they would go back.

Definition

Basic Principle of Counting

Example 3

Steve Wozniak, the co-founder Apple, was the first the person to own the phone number 888-888-8888. But it proved impossible to use, because he was receiving well over 100 wrong numbers a day; mostly from babies playing with the phone.

Example

Definition

Combinations

Formula

Combinations

Example 6

A student council consists of 12 members. A subcommittee of 4 members is to be chosen to organize a school event.

Example 7

A lottery requires players to select 6 numbers from a set of 49 numbers.

Example 8

A standard deck of 52 playing cards is shuffled, and players are dealt hands of 5 cards.

Definition

Permutation

Formula

Permutation of $n$ Distinct Objects

Formula

Permutation of $n$ Distinct Objects Taken $r$ at a Time

Example 9

At the race track, an exacta wager is a bet where the bettor picks the horse that will finish in first and second place. A trifecta is a bet where the bettor picks the horses that finish in first, second, and third place. If 12 horses enter a race,

Example 10

A credit card company requires that user set up a four-digit PIN number for security purposes.

Definition

Permutation of Similar Objects

Formula

Permutation of Similar Objects

Example 15

The Price is Right is a game show which offers contestants an opportunity to win prizes such as cars, trips, home appliances, and cash (mundane by today standards). Back in 1956, a contestant on the show won a grand piano, and as a joke the producers thought it would be funny to offer him a live elephant as the bonus prize; the real prize was $4000$ in cash. The joke backfired and the show was forced to ship in an elephant from Kenya.
Consider the word ELEPHANT.