{"id":869,"date":"2023-03-21T18:01:42","date_gmt":"2023-03-21T18:01:42","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/?post_type=chapter&p=869"},"modified":"2024-09-30T20:50:55","modified_gmt":"2024-09-30T20:50:55","slug":"applications-with-probability-learn-it-4","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/chapter\/applications-with-probability-learn-it-4\/","title":{"raw":"Applications With Probability: Learn It 4","rendered":"Applications With Probability: Learn It 4"},"content":{"raw":"

Combinations<\/h2>\r\n

When discussing permutations, we considered the situation where we chose [latex]r[\/latex] items out of [latex]n[\/latex] possibilities without replacement<\/em> and where the order of selection was important<\/em>. We now consider a similar situation in which the order of selection is not<\/em> important.<\/p>\r\n

\r\n
\r\n

combination<\/h3>\r\n

A combination is a selection of objects from a set without regard to the order in which they are selected.<\/p>\r\n

 <\/p>\r\n

Notation:<\/strong>The number of combinations of [latex]n[\/latex] objects taken [latex]r[\/latex] at a time is denoted by [latex] C(n, r)[\/latex] and is given by:<\/p>\r\n

 <\/p>\r\n

[latex] C(n, r) = \\frac{n!}{r!(n-r)!}[\/latex]<\/center><\/div>\r\n<\/section>\r\n
[ohm2_question hide_question_numbers=1]3287[\/ohm2_question]<\/section>\r\n
[videopicker divId=\"tnh-video-picker\" title=\"Permutations and Combinations\" label=\"Select Video\"]
\r\n[videooption displayName=\"How to Use Permutations and Combinations\" value=\"\/\/plugin.3playmedia.com\/show?mf=12431252&p3sdk_version=1.10.1&p=20361&pt=375&video_id=NEGxh_D7yKU&video_target=tpm-plugin-bl5shz40-NEGxh_D7yKU\"][videooption displayName=\"Permutation formula - Probability and combinatorics - Probability and Statistics - Khan Academy\" value=\"https:\/\/youtu.be\/DROZVHObeko\"] [videooption displayName=\"Permutations and Combinations Tutorial\" value=\"\/\/plugin.3playmedia.com\/show?mf=12431253&p3sdk_version=1.10.1&p=20361&pt=375&video_id=XJnIdRXUi7A&video_target=tpm-plugin-vvbxe1no-XJnIdRXUi7A\"]
\r\n[\/videopicker]\r\n\r\n\r\n

 <\/p>\r\n

You can view the transcript for \u201cHow to Use Permutations and Combinations\u201d here (opens in new window).<\/a><\/p>\r\n

You can view the transcript for \u201cPermutation formula | Probability and combinatorics | Probability and Statistics | Khan Academy\u201d here (opens in new window).<\/a><\/p>\r\n

You can view the transcript for \u201cPermutations and Combinations Tutorial\u201d here (opens in new window).<\/a><\/p>\r\n<\/section>","rendered":"

Combinations<\/h2>\n

When discussing permutations, we considered the situation where we chose [latex]r[\/latex] items out of [latex]n[\/latex] possibilities without replacement<\/em> and where the order of selection was important<\/em>. We now consider a similar situation in which the order of selection is not<\/em> important.<\/p>\n

\n
\n

combination<\/h3>\n

A combination is a selection of objects from a set without regard to the order in which they are selected.<\/p>\n

 <\/p>\n

Notation:<\/strong>The number of combinations of [latex]n[\/latex] objects taken [latex]r[\/latex] at a time is denoted by [latex]C(n, r)[\/latex] and is given by:<\/p>\n

 <\/p>\n

[latex]C(n, r) = \\frac{n!}{r!(n-r)!}[\/latex]<\/div>\n<\/div>\n<\/section>\n