If one event can occur in [latex]m[\/latex] ways and a second event with no common outcomes can occur in [latex]n[\/latex] ways, then the first or second event can occur in [latex]m+n[\/latex] ways.<\/li>\n\t
If one event can occur in [latex]m[\/latex] ways and a second event can occur in [latex]n[\/latex] ways after the first event has occurred, then the two events can occur in [latex]m\\times n[\/latex] ways.<\/li>\n\t
A permutation is an ordering of [latex]n[\/latex] objects.<\/li>\n\t
If we have a set of [latex]n[\/latex] objects and we want to choose [latex]r[\/latex] objects from the set in order, we write [latex]P\\left(n,r\\right)[\/latex].<\/li>\n\t
Permutation problems can be solved using the Multiplication Principle or the formula for [latex]P\\left(n,r\\right)[\/latex].<\/li>\n\t
A selection of objects where the order does not matter is a combination.<\/li>\n\t
Given [latex]n[\/latex] distinct objects, the number of ways to select [latex]r[\/latex] objects from the set is [latex]\\text{C}\\left(n,r\\right)[\/latex] and can be found using a formula.<\/li>\n\t
A set containing [latex]n[\/latex] distinct objects has [latex]{2}^{n}[\/latex] subsets.<\/li>\n\t
For counting problems involving non-distinct objects, we need to divide to avoid counting duplicate permutations.<\/li>\n<\/ul>
Glossary<\/h2>\n
Addition Principle<\/dt>
if one event can occur in [latex]m[\/latex] ways and a second event with no common outcomes can occur in [latex]n[\/latex] ways, then the first or second event can occur in [latex]m+n[\/latex] ways<\/dd><\/dl>
combination<\/dt>
a selection of objects in which order does not matter<\/dd><\/dl>
Fundamental Counting Principle<\/dt>
if one event can occur in [latex]m[\/latex] ways and a second event can occur in [latex]n[\/latex] ways after the first event has occurred, then the two events can occur in [latex]m\\times n[\/latex] ways; also known as the Multiplication Principle<\/dd><\/dl>
Multiplication Principle<\/dt>
if one event can occur in [latex]m[\/latex] ways and a second event can occur in [latex]n[\/latex] ways after the first event has occurred, then the two events can occur in [latex]m\\times n[\/latex] ways; also known as the Fundamental Counting Principle<\/dd><\/dl>
permutation<\/dt>
a selection of objects in which order matters<\/dd><\/dl>\u00a0","rendered":"
Key Equations<\/h2>\n
\n\n
\n
number of permutations of [latex]n[\/latex] distinct objects taken [latex]r[\/latex] at a time<\/td>\n
If one event can occur in [latex]m[\/latex] ways and a second event with no common outcomes can occur in [latex]n[\/latex] ways, then the first or second event can occur in [latex]m+n[\/latex] ways.<\/li>\n
If one event can occur in [latex]m[\/latex] ways and a second event can occur in [latex]n[\/latex] ways after the first event has occurred, then the two events can occur in [latex]m\\times n[\/latex] ways.<\/li>\n
A permutation is an ordering of [latex]n[\/latex] objects.<\/li>\n
If we have a set of [latex]n[\/latex] objects and we want to choose [latex]r[\/latex] objects from the set in order, we write [latex]P\\left(n,r\\right)[\/latex].<\/li>\n
Permutation problems can be solved using the Multiplication Principle or the formula for [latex]P\\left(n,r\\right)[\/latex].<\/li>\n
A selection of objects where the order does not matter is a combination.<\/li>\n
Given [latex]n[\/latex] distinct objects, the number of ways to select [latex]r[\/latex] objects from the set is [latex]\\text{C}\\left(n,r\\right)[\/latex] and can be found using a formula.<\/li>\n
A set containing [latex]n[\/latex] distinct objects has [latex]{2}^{n}[\/latex] subsets.<\/li>\n
For counting problems involving non-distinct objects, we need to divide to avoid counting duplicate permutations.<\/li>\n<\/ul>\n
Glossary<\/h2>\n
\n
Addition Principle<\/dt>\n
if one event can occur in [latex]m[\/latex] ways and a second event with no common outcomes can occur in [latex]n[\/latex] ways, then the first or second event can occur in [latex]m+n[\/latex] ways<\/dd>\n<\/dl>\n
\n
combination<\/dt>\n
a selection of objects in which order does not matter<\/dd>\n<\/dl>\n
\n
Fundamental Counting Principle<\/dt>\n
if one event can occur in [latex]m[\/latex] ways and a second event can occur in [latex]n[\/latex] ways after the first event has occurred, then the two events can occur in [latex]m\\times n[\/latex] ways; also known as the Multiplication Principle<\/dd>\n<\/dl>\n
\n
Multiplication Principle<\/dt>\n
if one event can occur in [latex]m[\/latex] ways and a second event can occur in [latex]n[\/latex] ways after the first event has occurred, then the two events can occur in [latex]m\\times n[\/latex] ways; also known as the Fundamental Counting Principle<\/dd>\n<\/dl>\n
\n
permutation<\/dt>\n
a selection of objects in which order matters<\/dd>\n<\/dl>\n