1Cn

{ "query": { "display": "1Cn", "symbolab_question": "#1Cn" }, "solution": { "level": "PERFORMED", "subject": "Statistics", "topic": "nCr", "subTopic": "Other", "default": "\\frac{1}{n!(1-n)!}" }, "steps": { "type": "interim", "title": "$$1\\:nCr\\:n:{\\quad}\\frac{1}{n!\\left(1-n\\right)!}$$", "steps": [ { "type": "definition", "title": "n choose r", "text": "Gives the number of subsets of r elements, out of n elements<br/>$$nCr=\\frac{n!}{r!\\left(n-r\\right)!}$$" }, { "type": "step", "result": "=\\frac{n!}{r!\\left(n-r\\right)!}" }, { "type": "step", "primary": "Plug in $$n=1,\\:r=n$$", "result": "=\\frac{1!}{n!\\left(1-n\\right)!}" }, { "type": "interim", "title": "Simplify $$\\frac{1!}{n!\\left(1-n\\right)!}:{\\quad}\\frac{1}{n!\\left(1-n\\right)!}$$", "input": "\\frac{1!}{n!\\left(1-n\\right)!}", "result": "=\\frac{1}{n!\\left(1-n\\right)!}", "steps": [ { "type": "step", "primary": "Apply factorial rule: $$n!=1\\cdot2\\cdot3\\cdot\\ldots\\cdot\\:n$$", "secondary": [ "$$1!=1$$" ], "result": "=\\frac{1}{n!\\left(-n+1\\right)!}" } ], "meta": { "solvingClass": "Solver" } } ] } }