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*Probability Permutations and Combinations. Permutations are known as any arrangement of distinct...*

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ProbabilityPermutations and Combinations

Permutations Permutations are known as any arrangement of distinct objects in a particular _________.order

Example 1A doctor has six examination rooms. There are six patients in a waiting room. In how many different ways can the patients be assigned to the examination rooms?

Room 1Room 2Room 3Room 4Room 5Room 6

FactorialA ______ is used to represent a factorial. A factorial is a type of repeated ________________.

For example.multiplication

Permutation NotationPermutations are solved using the formula

Like any formula we will use we need to know what the variables are!n represents the total number of thingsr represents the number taken at a time

Example 2A baseball scout has received a list of 15 promising prospects. The scout is asked to list, in order of preference, the five most outstanding of these prospects. In how many different ways can the scout select the five best players?Total Number (n)Number Chosen (r)

Example 3How many different permutations are there of the letters in the words?MATHEMATICSTotal Number (n)Number Chosen (r)

Example 3bHow many different permutations are there of the letters in the words?MISSISSIPITotal Number (n)Number Chosen (r)

CombinationsCombinations are a collection of distinct objects where ________ is _______ important.

The number of combinations of things taken at a time where order is not important is denoted:

ordernot

Example 4How many different 11-member football teams can be formed from a possible 20 players if any player can play any position?Total Number (n)Number Chosen (r)

Example 5How many different poker hands consisting of five cards can be dealt from a deck of 52 cards?Total Number (n)Number Chosen (r)

Example 5bWhat is the probability of being dealt a royal flush in five-card poker?

4 ways to draw with 4 suits

Example 6John has ten single dollar bills of which three are counterfeit. If he selects four of them at random, what is the probability of getting two good bills and two counterfeit bills?

We need to figure out a few different things to set up a full probability!

Example 6Start with how many ways you can choose 4 bills from a possible 10.

Example 6Next we need how many ways 2 cards can be chosen from the 7 good cards.

Example 6Finally, we need to know how 2 counterfeit cards can be selected from 3.

Example 6Now we put it all together!