// Numbas version: finer_feedback_settings
{"name": "Kombinatorikk", "extensions": [], "custom_part_types": [], "resources": [["question-resources/mulige_ord.PNG", "mulige_ord.PNG"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Kombinatorikk", "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p>Det er gitt tre symboler $a$, $b$ og $c$. Med disse symbolene er det mulig &aring; lage $3\\cdot 3=9$ \"ord\" av lengde 2, nemlig</p>\n<p>$aa,\\ ab,\\ ac,\\ ba,\\ bb,\\ bc,\\ ca,\\ cb,\\ cc$</p>", "advice": "<p>a) <span class=\"textLayer--absolute\">Her </span><span class=\"textLayer--absolute\">kan </span><span class=\"textLayer--absolute\">man gj&oslash;re som i f&oslash;rste oppgave &aring; skrive ned alle mulighe</span><span class=\"textLayer--absolute\">tene </span></p>\n<p><span class=\"textLayer--absolute\">$aaa;\\ aab;\\ aac;\\ aba;\\ abb;\\ abc;\\ aca;\\ acb;\\ acc;\\ baa;\\ bab;\\ bac;\\ bba;\\ bbb;\\ bbc;\\ bca;\\ bcb;\\ bcc;\\ caa;\\ cab;\\ cac;\\ cba;\\ cbb;\\ cbc;\\ cca;\\ ccb;\\ ccc&nbsp;$</span></p>\n<p><span class=\"textLayer--absolute\">s&aring; totalt </span><span class=\"textLayer--absolute\">27</span><span class=\"textLayer--absolute\">. </span></p>\n<p><span class=\"textLayer--absolute\">Alternativt kan vi og telle hvor mange muligheter vi har p&aring; hver</span><span class=\"textLayer--absolute\">plass. For den f&oslash;rste bokstaven har vi tre muligheter $</span><span class=\"textLayer--absolute\">abc$</span><span class=\"textLayer--absolute\">, for den neste bokstaven</span><span class=\"textLayer--absolute\">har vi n&aring; ogs&aring; </span><span class=\"textLayer--absolute\">3 </span><span class=\"textLayer--absolute\">muligheter og endelig for den siste bokstaven har vi ogs&aring; </span><span class=\"textLayer--absolute\">3 </span><span class=\"textLayer--absolute\">muligheter. Totalt $3\\cdot3\\cdot3=27$ </span><span class=\"textLayer--absolute\">muligheter. Her kan og </span><span class=\"textLayer--absolute\">figur nedenfor v</span><span class=\"textLayer--absolute\">&aelig;re til </span><span class=\"textLayer--absolute\">hjelp. For hvert nye niv&aring; for hver av v&aring;re opprinnelige ord, tre nye ord de kan </span><span class=\"textLayer--absolute\">bli til.</span></p>\n<p><span class=\"textLayer--absolute\"><img src=\"resources/question-resources/mulige_ord.PNG\"/></span></p>\n<p><span class=\"textLayer--absolute\">b) Slik som vi nevnte i forrige deloppgave og som illustrert i figur f&aring;r vi tre nye muligheter for hvert ord vi har. Dersom vi har $n$ ord, eller ett ord av lengde $n$ s&aring; kan vi totalt lage </span></p>\n<p>$\\underbrace{3\\cdot3\\cdot\\ldots\\cdot3}_\\text{n ganger}=3^n$ mulige ord.</p>", "rulesets": {}, "extensions": [], "variables": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Hvor mange ord av lengde 3 kan man lage?</p>", "minValue": "27", "maxValue": "27", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Hvor mange ord av lengde $n$ kan man lage?</p>", "answer": "3^n", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "n", "value": ""}]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question", "contributors": [{"name": "Elena Malyutina", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7213/"}], "resources": ["question-resources/mulige_ord.PNG"]}]}], "contributors": [{"name": "Elena Malyutina", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7213/"}]}