{ "query": { "display": "P(12, 9)", "symbolab_question": "#P(12,9)" }, "solution": { "level": "PERFORMED", "subject": "Statistics", "topic": "nCr", "subTopic": "Other", "default": "79833600" }, "steps": { "type": "interim", "title": "$$12\\:nPr\\:9:{\\quad}79833600$$", "steps": [ { "type": "definition", "title": "n choose r", "text": "The number of possibilities for choosing an ordered set of r objects from a total of n objects<br/>$$nPr=\\frac{n!}{\\left(n-r\\right)!}$$" }, { "type": "step", "result": "=\\frac{n!}{\\left(n-r\\right)!}" }, { "type": "step", "primary": "Plug in $$n=12,\\:r=9$$", "result": "=\\frac{12!}{\\left(12-9\\right)!}" }, { "type": "interim", "title": "$$\\frac{12!}{\\left(12-9\\right)!}=79833600$$", "input": "\\frac{12!}{\\left(12-9\\right)!}", "result": "=79833600", "steps": [ { "type": "step", "primary": "Subtract the numbers: $$12-9=3$$", "result": "=\\frac{12!}{3!}" }, { "type": "step", "primary": "Cancel the factorials: $$\\frac{n!}{\\left(n-m\\right)!}=n\\cdot\\left(n-1\\right)\\cdots\\left(n-m+1\\right),\\:n>m$$", "secondary": [ "$$\\frac{12!}{3!}=12\\cdot\\:11\\cdot\\:10\\cdot\\:9\\cdot\\:8\\cdot\\:7\\cdot\\:6\\cdot\\:5\\cdot\\:4$$" ], "result": "=12\\cdot\\:11\\cdot\\:10\\cdot\\:9\\cdot\\:8\\cdot\\:7\\cdot\\:6\\cdot\\:5\\cdot\\:4" }, { "type": "step", "primary": "Refine", "result": "=79833600" } ], "meta": { "solvingClass": "Solver" } } ] } }