{ "query": { "display": "p(8, 4)", "symbolab_question": "#p(8,4)" }, "solution": { "level": "PERFORMED", "subject": "Statistics", "topic": "nCr", "subTopic": "Other", "default": "1680" }, "steps": { "type": "interim", "title": "$$8\\:nPr\\:4:{\\quad}1680$$", "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 $$n=8,\\:r=4$$", "result": "=\\frac{8!}{\\left(8-4\\right)!}" }, { "type": "interim", "title": "$$\\frac{8!}{\\left(8-4\\right)!}=1680$$", "input": "\\frac{8!}{\\left(8-4\\right)!}", "result": "=1680", "steps": [ { "type": "step", "primary": "Subtract the numbers: $$8-4=4$$", "result": "=\\frac{8!}{4!}" }, { "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": [ "$$\\frac{8!}{4!}=8\\cdot\\:7\\cdot\\:6\\cdot\\:5$$" ], "result": "=8\\cdot\\:7\\cdot\\:6\\cdot\\:5" }, { "type": "step", "primary": "Refine", "result": "=1680" } ], "meta": { "solvingClass": "Solver" } } ] } }