((Combinatorics Final Exam:: 2026- 2027.))
Combinatorics Final Exam, Key Concepts
Study online at https://quizlet.com/_iget7i
1. Hypergeometric A probability distribution that describes the likelihood of obtaining a specific num-
Distribution ber of successes in a sample drawn without replacement from a finite population
containing a fixed number of successes and failures. In Fisher's exact test, it models
the possible cell counts in a contingency table when the margins are fixed.
2. Multinomial Sam- Multinomial sampling is a method where each observation falls into one of several
pling categories, and the total number of observations is fixed in advance. The count in
each category follows a multinomial distribution.
3. Hypergeometric A hypergeometric exact p-value is the probability of observing data as extreme
Exact P-Value or more extreme than actually observed, under the null hypothesis, using the
hypergeometric distribution. It is used in Fisher’s Exact Test for paired categorical
data to assess statistical significance.
4. Number of Classi- The number of classifiers refers to how many binary classifiers are needed in a
fiers multiclass one-versus-one strategy. For k classes, this number is k(k-1)/2, repre-
senting all possible class pairs.
5. K-Factor Factorial A k-factor factorial treatment structure describes an experiment that includes k
Treatment Struc- different factors, each with its own set of levels, and considers all possible combi-
ture nations of these levels.
6. Core Model Con- Latin Square Design is an experimental design used to control for two sources of
cepts of Latin variability (often called row and column effects) in addition to the treatment effects.
Square Design Each treatment appears exactly once in every row and every column. This helps to
eliminate the possible confounding effects of two different blocking factors while
testing the treatments.
7. Latin Square De- A Latin square design is an experimental layout with k treatments arranged in a k by
sign (k Times k) k grid, where each treatment appears exactly once in every row and every column.
It helps control for two sources of variability, such as row and column effects.
Page 1 of 12 3/31/2026
, ((Combinatorics Final Exam:: 2026- 2027.))
Combinatorics Final Exam, Key Concepts
Study online at https://quizlet.com/_iget7i
8. Equal Probability Equal probability selection means that each member of the population has the
Selection same likelihood of being included in the sample.
9. Selection Proba- Selection probability is the chance that a specific element is chosen during the
bility sampling process.
10. Conditional Prob- Conditional probability is the chance that one event happens given that another
ability and Inde- event has already occurred. Independence means that the occurrence of one event
pendence does not affect the probability of another event happening.
11. Event Indepen- Event independence by outcome counts checks if the number of outcomes where
dence by Out- both events happen matches what is expected if the events were independent.
come Counts
12. Counting Tech- Counting techniques and combinatorics are methods used to count possible
niques and Com- outcomes in a systematic way. They include rules like the multiplication and ad-
binatorics dition principles, as well as permutations and combinations, which help calculate
probabilities in complex situations.
13. Basic Principles The basic principles of counting are fundamental rules used to determine the
of Counting number of possible outcomes in a sequence of events. The two main principles
are the addition rule, used when events cannot happen at the same time, and the
multiplication rule, used when events happen in sequence.
14. Addition The Addition Principle says that if there are two events that cannot happen at the
Principle and same time, the total number of ways either event can occur is the sum of the ways
Inclusion-Exclu- each can occur. The Inclusion-Exclusion Principle adjusts for overlap by subtracting
sion Basics the number of outcomes shared by both events, to avoid double-counting.
15. Addition Rule for The addition rule for counting states that if two or more events cannot happen at
Counting the same time, the total number of ways either event can occur is the sum of the
number of ways each event can occur separately.
16.
Page 2 of 12 3/31/2026
Combinatorics Final Exam, Key Concepts
Study online at https://quizlet.com/_iget7i
1. Hypergeometric A probability distribution that describes the likelihood of obtaining a specific num-
Distribution ber of successes in a sample drawn without replacement from a finite population
containing a fixed number of successes and failures. In Fisher's exact test, it models
the possible cell counts in a contingency table when the margins are fixed.
2. Multinomial Sam- Multinomial sampling is a method where each observation falls into one of several
pling categories, and the total number of observations is fixed in advance. The count in
each category follows a multinomial distribution.
3. Hypergeometric A hypergeometric exact p-value is the probability of observing data as extreme
Exact P-Value or more extreme than actually observed, under the null hypothesis, using the
hypergeometric distribution. It is used in Fisher’s Exact Test for paired categorical
data to assess statistical significance.
4. Number of Classi- The number of classifiers refers to how many binary classifiers are needed in a
fiers multiclass one-versus-one strategy. For k classes, this number is k(k-1)/2, repre-
senting all possible class pairs.
5. K-Factor Factorial A k-factor factorial treatment structure describes an experiment that includes k
Treatment Struc- different factors, each with its own set of levels, and considers all possible combi-
ture nations of these levels.
6. Core Model Con- Latin Square Design is an experimental design used to control for two sources of
cepts of Latin variability (often called row and column effects) in addition to the treatment effects.
Square Design Each treatment appears exactly once in every row and every column. This helps to
eliminate the possible confounding effects of two different blocking factors while
testing the treatments.
7. Latin Square De- A Latin square design is an experimental layout with k treatments arranged in a k by
sign (k Times k) k grid, where each treatment appears exactly once in every row and every column.
It helps control for two sources of variability, such as row and column effects.
Page 1 of 12 3/31/2026
, ((Combinatorics Final Exam:: 2026- 2027.))
Combinatorics Final Exam, Key Concepts
Study online at https://quizlet.com/_iget7i
8. Equal Probability Equal probability selection means that each member of the population has the
Selection same likelihood of being included in the sample.
9. Selection Proba- Selection probability is the chance that a specific element is chosen during the
bility sampling process.
10. Conditional Prob- Conditional probability is the chance that one event happens given that another
ability and Inde- event has already occurred. Independence means that the occurrence of one event
pendence does not affect the probability of another event happening.
11. Event Indepen- Event independence by outcome counts checks if the number of outcomes where
dence by Out- both events happen matches what is expected if the events were independent.
come Counts
12. Counting Tech- Counting techniques and combinatorics are methods used to count possible
niques and Com- outcomes in a systematic way. They include rules like the multiplication and ad-
binatorics dition principles, as well as permutations and combinations, which help calculate
probabilities in complex situations.
13. Basic Principles The basic principles of counting are fundamental rules used to determine the
of Counting number of possible outcomes in a sequence of events. The two main principles
are the addition rule, used when events cannot happen at the same time, and the
multiplication rule, used when events happen in sequence.
14. Addition The Addition Principle says that if there are two events that cannot happen at the
Principle and same time, the total number of ways either event can occur is the sum of the ways
Inclusion-Exclu- each can occur. The Inclusion-Exclusion Principle adjusts for overlap by subtracting
sion Basics the number of outcomes shared by both events, to avoid double-counting.
15. Addition Rule for The addition rule for counting states that if two or more events cannot happen at
Counting the same time, the total number of ways either event can occur is the sum of the
number of ways each event can occur separately.
16.
Page 2 of 12 3/31/2026
