{"id":840,"date":"2023-03-21T16:18:36","date_gmt":"2023-03-21T16:18:36","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/?post_type=chapter&p=840"},"modified":"2023-11-17T15:33:35","modified_gmt":"2023-11-17T15:33:35","slug":"applications-with-probability-learn-it-3","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/chapter\/applications-with-probability-learn-it-3\/","title":{"raw":"Applications With Probability: Learn It 3","rendered":"Applications With Probability: Learn It 3"},"content":{"raw":"

Permutations<\/h2>\r\n

Before we dive into permutations, it is important to understand how to take a factorial<\/strong>.<\/p>\r\n

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\r\n

factorial<\/h3>\r\n

Calculating the factorial <\/strong>is a way to calculate the product of all positive whole numbers up to a given number.<\/p>\r\n

 <\/p>\r\n

Notation:<\/strong> A factorial is represented by an exclamation mark [latex](!)[\/latex] following a number.<\/p>\r\n

 <\/p>\r\n

[latex] n! = n \\cdot (n-1)\\cdot (n-2)...1[\/latex]<\/center><\/div>\r\n<\/section>\r\n
[ohm2_question hide_question_numbers=1]2854[\/ohm2_question]<\/section>\r\n
[ohm2_question hide_question_numbers=1]3284[\/ohm2_question]<\/section>\r\n

Now that we understand how to take a factorial, lets see how it applies to permutations<\/strong>.<\/p>\r\n

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permutation<\/h3>\r\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>\r\n

 <\/p>\r\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>\r\n

 <\/p>\r\n

[latex] P(n, r) = \\frac{n!}{(n-r)!}[\/latex]<\/center><\/div>\r\n<\/section>\r\n
Jayden has nine paintings and only has room on their wall for four paintings. How many different ways could they select paintings for their wall?
\r\n[reveal-answer q=\"366612\"]Show Solution[\/reveal-answer]
\r\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,
[latex]\\begin{array}{ll} P(n, r)& = \\frac{n!}{(n-r)!} \\\\
\r\n& = \\frac{9!}{(9-4)!} \\\\
\r\n& = \\frac{9!}{5!} \\\\
\r\n& = \\frac{362,880}{120} \\\\
\r\n& = 3,024 \\text{ permutations} \\end{array}[\/latex]<\/center>[\/hidden-answer]<\/section>\r\n
[ohm2_question hide_question_numbers=1]3286[\/ohm2_question]<\/section>","rendered":"

Permutations<\/h2>\n

Before we dive into permutations, it is important to understand how to take a factorial<\/strong>.<\/p>\n

\n
\n

factorial<\/h3>\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

[latex]n! = n \\cdot (n-1)\\cdot (n-2)...1[\/latex]<\/div>\n<\/div>\n<\/section>\n