2P2

{ "query": { "display": "2P2", "symbolab_question": "#2P2" }, "solution": { "level": "PERFORMED", "subject": "Statistics", "topic": "nCr", "subTopic": "Other", "default": "2" }, "steps": { "type": "interim", "title": "$$2\\:nPr\\:2:{\\quad}2$$", "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 $$n=2,\\:r=2$$", "result": "=\\frac{2!}{\\left(2-2\\right)!}" }, { "type": "interim", "title": "$$\\frac{2!}{\\left(2-2\\right)!}=2$$", "input": "\\frac{2!}{\\left(2-2\\right)!}", "result": "=2", "steps": [ { "type": "interim", "title": "$$\\left(2-2\\right)!=1$$", "input": "\\left(2-2\\right)!", "steps": [ { "type": "step", "primary": "Subtract the numbers: $$2-2=0$$", "result": "=0!" }, { "type": "step", "primary": "Apply factorial rule: $$0!=1$$", "result": "=1" } ], "meta": { "solvingClass": "Solver" } }, { "type": "step", "result": "=\\frac{2!}{1}" }, { "type": "step", "primary": "Apply rule $$\\frac{a}{1}=a$$", "result": "=2!" }, { "type": "step", "primary": "Apply factorial rule: $$n!=1\\cdot2\\cdot3\\cdot\\ldots\\cdot\\:n$$", "secondary": [ "$$2!=1\\cdot\\:2$$" ], "result": "=1\\cdot\\:2" }, { "type": "step", "primary": "Multiply the numbers: $$1\\cdot\\:2=2$$", "result": "=2" } ], "meta": { "solvingClass": "Solver" } } ] } }