Sports CampSports CampMorning CampMorning Camp

AerobicsAerobicsRunningRunning

YogaYogaSwimmingSwimmingWeightsWeights

Afternoon CampAfternoon Camp

HikingHiking

TennisTennis

VolleyballVolleyball

SoftballSoftball

List all the possible choices List all the possible choices available on your paperavailable on your paper

Terminology of CountingTerminology of Counting1)1) Tree DiagramTree Diagram

2)2) OutcomeOutcome – number of ways it can – number of ways it can occur. Each individual mix is an occur. Each individual mix is an outcome.outcome.

3)3) EventEvent – situation requiring choices – situation requiring choices

(morning events, afternoon events)(morning events, afternoon events)

4)4) Independent eventIndependent event – an event that – an event that does not affect or involve another does not affect or involve another event. Does not affect the outcome event. Does not affect the outcome of a different event.of a different event.

How many events? Outcomes?How many events? Outcomes?Diagram itDiagram it

1.1. Flip a coin, then roll a number Flip a coin, then roll a number cube? Show all outcomes.cube? Show all outcomes.

2.2. Choose from 5 movies, then from 3 Choose from 5 movies, then from 3 restaurants? Show all outcomes.restaurants? Show all outcomes.

3.3. Choose from 3 new vehicles and Choose from 3 new vehicles and colors white, black or blue. Show all colors white, black or blue. Show all outcomes.outcomes.

4.4. Roll a number cube, then pick a Roll a number cube, then pick a card from a deck of cards?card from a deck of cards?

How many outcomes? Events?How many outcomes? Events?

1.1. Roll a number cube 4 times. How many Roll a number cube 4 times. How many possible?possible?

2.2. License plates – 4 letters and 3 numbers. License plates – 4 letters and 3 numbers. How many possible (can repeat #s and How many possible (can repeat #s and letters)?letters)?

3.3. Social security number – 9 digits, all Social security number – 9 digits, all repeatable. How many possible?repeatable. How many possible?

4.4. Social security number – 1Social security number – 1stst and last and last digits must be 1 or 0. Other 7 may be digits must be 1 or 0. Other 7 may be anything. How many possible?anything. How many possible?

Counting PrincipleCounting Principle

If one event occurs ‘m’ ways and If one event occurs ‘m’ ways and second event occurs ‘n’ ways, then second event occurs ‘n’ ways, then the 2 events occurthe 2 events occur

n * m waysn * m ways

Provided the events are independent Provided the events are independent of each other.of each other.

PermutationsPermutations

How many outcomes?How many outcomes?

1)1) 18 bands compete to win 118 bands compete to win 1stst, 2, 2ndnd, , 33rdrd, and 4, and 4thth place. How many place. How many outcomes possible?outcomes possible?

2)2) President, vice-president, treasurer President, vice-president, treasurer chosen from a class of 520. How chosen from a class of 520. How many outcomes possible?many outcomes possible?

On these questions, does order On these questions, does order matter?matter?

PermutationsPermutations

Arrangement of a group of objects in a Arrangement of a group of objects in a particular order. (order matters!)particular order. (order matters!)

20 choose 3:20 choose 3: means means 20 20 * * 19 19 * * 18 18

Also written as Also written as 2020PP33 which means which means

20!20!(20-3)!(20-3)!