{ "query": { "display": "P(4, 2)", "symbolab_question": "#P(4,2)" }, "solution": { "level": "PERFORMED", "subject": "Statistics", "topic": "nCr", "subTopic": "Other", "default": "12" }, "steps": { "type": "interim", "title": "$$4\\:nPr\\:2:{\\quad}12$$", "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 $$n=4,\\:r=2$$", "result": "=\\frac{4!}{\\left(4-2\\right)!}" }, { "type": "interim", "title": "$$\\frac{4!}{\\left(4-2\\right)!}=12$$", "input": "\\frac{4!}{\\left(4-2\\right)!}", "result": "=12", "steps": [ { "type": "step", "primary": "Subtract the numbers: $$4-2=2$$", "result": "=\\frac{4!}{2!}" }, { "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": [ "$$\\frac{4!}{2!}=4\\cdot\\:3$$" ], "result": "=4\\cdot\\:3" }, { "type": "step", "primary": "Refine", "result": "=12" } ], "meta": { "solvingClass": "Solver" } } ] } }