Before we dive into permutations, it is important to understand how to take a factorial<\/strong>.<\/p>\n Calculating the factorial <\/strong>is a way to calculate the product of all positive whole numbers up to a given number.<\/p>\n <\/p>\n Notation:<\/strong> A factorial is represented by an exclamation mark [latex](!)[\/latex] following a number.<\/p>\n <\/p>\n Now that we understand how to take a factorial, lets see how it applies to permutations<\/strong>.<\/p>\n A permutation <\/strong>is an arrangement of a set of objects in a particular order. In permutations, the order in which the objects are arranged is important.<\/p>\n <\/p>\n Notation:<\/strong> The number of permutations of [latex]n[\/latex] objects taken [latex]r[\/latex] at a time is denoted by [latex] P(n, r)[\/latex] and is given by:<\/p>\n <\/p>\n Before we dive into permutations, it is important to understand how to take a factorial<\/strong>.<\/p>\n Calculating the factorial <\/strong>is a way to calculate the product of all positive whole numbers up to a given number.<\/p>\n <\/p>\n Notation:<\/strong> A factorial is represented by an exclamation mark [latex](!)[\/latex] following a number.<\/p>\n <\/p>\nfactorial<\/h3>\n
permutation<\/h3>\n
\n[reveal-answer q=\"366612\"]Show Solution[\/reveal-answer]
\n[hidden-answer a=\"366612\"]Since Jayden is choosing [latex]4[\/latex] paintings out of [latex]9[\/latex] without replacement<\/em> where the order of selection is important<\/em> we can apply our permutation rule to solve this. In this example [latex]n[\/latex] is [latex]9[\/latex] and [latex]r[\/latex] is [latex]4[\/latex] therefore,
\n& = \\frac{9!}{(9-4)!} \\\\
\n& = \\frac{9!}{5!} \\\\
\n& = \\frac{362,880}{120} \\\\
\n& = 3,024 \\text{ permutations} \\end{array}[\/latex]<\/center>[\/hidden-answer]<\/section>\nPermutations<\/h2>\n
factorial<\/h3>\n