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Section 1.5 Combinatorics: First Counts
Combinatorics is the mathematics of counting.
Subsection 1.5.1 Terminology
Alphabet is an undefined term referring to a set of objects typically thought of as symbols such as the alphabets used in western European languages, Cyrillic, digits of numbers, or emojis.
Definition 1.5.1 . String/Word.
A
string or
word is an ordered set of characters from an alphabet.
A few words from the alphabet { a,b,c } are the following: c, abc, bc, cab, ccb, aaa. A few words from the alphabet
\(\{0,1,2,3,4,5,6,7,8,9\}\) are 301, 112, 5.
Definition 1.5.2 . Permutation.
A
permutation of a string is any arrangement of the characters in that string including the same order.
A few of the permutations of the string βabcβ are: abc, bac, cab.
Subsection 1.5.2 Practice
Checkpoint 1.5.3 .
Generate a list of all possible strings of length two from the alphabet
\(\{0,1\}.\)
Checkpoint 1.5.4 .
How many strings of length three are possible from the alphabet
\(\{0,1\}\text{?}\) Do not use a formula.
Checkpoint 1.5.5 .
How many strings of length three are possible from the alphabet
\(\{0,1,2\}\text{?}\) Do not use a formula.
Checkpoint 1.5.6 .
Write all permutations of the string βmatβ.
Checkpoint 1.5.7 .
How many permutations are there of the string βeatβ.
Checkpoint 1.5.8 .
Write all permutations of the string βmathβ.
Checkpoint 1.5.9 .
How many permutations are there of the string βheatβ.
Checkpoint 1.5.10 .
How many permutations are there of the string βgreatβ.