Selecting Lottery Entries In SuperLotto Plus, a California state lottery game, you select five distinct numbers from 1 to 47, and one MEGA number from 1 to 27, hoping that your selection will match a random list selected by lottery officials. (a) How ma

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FUNDAMENTAL COUNTING PRINCIPLE
When a task consists of k separate parts, where
represents the number of ways to complete the
first part, represents the number of ways to
complete the second part, represents the number
of ways to complete the third part, etc. The
total number of ways to complete the task is.
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Example 1) A restaurant runs a lunch special
consisting of a choice of appetizer, entrée,
dessert and drink. How many different meal
combinations are possible if a customer can
choose from 5 appetizers, 10 entrees, 7 desserts
and 4 drinks? TASK PARTS
WAYS TO COMPLETE EACH PART
Total possible meal
combinations Can the same items be used for
different parts?
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Example 1) A restaurant runs a lunch special
consisting of a choice of appetizer, entrée,
dessert and drink. How many different meal
combinations are possible if a customer can
choose from 5 appetizers, 10 entrees, 7 desserts
and 4 drinks? TASK Calculate total number of
possible meal combinations PARTS 4
WAYS TO COMPLETE EACH PART
Total possible meal
combinations 1400 Can the same items be used
for different parts? No
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FUNDAMENTAL COUNTING PRINCIPLE EXTENSION
If the number of ways to complete each part are
drawn from the same population AND each way can
only be used once, then for a task with k parts,
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Example 2) Ten students are running for class
office. In the election, the person with the
most votes is elected president, second most is
vice president, third most is treasurer and
fourth most is secretary. How many different
election results are possible? TASK PARTS
WAYS TO COMPLETE EACH PART
Total possible election
results Can the same items be used for
different parts?
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Example 2) Ten students are running for class
office. In the election, the person with the
most votes is elected president, second most is
vice president, third most is treasurer and
fourth most is secretary. How many different
election results are possible? TASK Calculate
the total number of possible election
results PARTS 4
WAYS TO COMPLETE EACH PART
Total possible election
results 5040 Can the same items be used for
different parts? Yes
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Practice Problems
1. How many two digit numbers are there in the
base 8 number system?
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Practice Problems
2. Find the number of two digit numbers in the
base 12 number system that do not contain
repeated digits
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Practice Problems
3. Find the number of ways club N(Peter, Dan,
Mary and Carl) can elect a president and a
secretary if no one may hold more than one office
and the secretary must be a male.
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Practice Problems
4. How many odd three-digit counting numbers,
where no digit is repeated, are there in the
standard base ten number system?
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Practice Problems
5. In some states, auto license plates have
three letters followed by three digits. How many
such license plates are possible?
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Practice Problems
6. A four digit number is to be constructed
using only the digits from the set 1, 2, 3.
How many such numbers are possible? How many of
these are odd numbers less than 2000?
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Practice Problems
7. Vern has four antique wood golf clubs that he
wants to give to his three sons, Mark, Chris and
Scott. How many ways can the clubs be
distributed?
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Practice Problems
8. Vern has four antique wood golf clubs that he
wants to give to his three sons, Mark, Chris and
Scott. If the power driver must go to Mark and
the three wood must go to either Chris or Scott,
how many ways can the clubs be distributed?