Definition 1.5.1. String/Word.
A string or word is an ordered set of characters from an alphabet.
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.
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 “abc” 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 “mat”.
Checkpoint 1.5.7.
How many permutations are there of the string “eat”.
Checkpoint 1.5.8.
Write all permutations of the string “math”.
Checkpoint 1.5.9.
How many permutations are there of the string “heat”.
Checkpoint 1.5.10.
How many permutations are there of the string “great”.
