2 cm

{ "query": { "display": "2 cm", "symbolab_question": "#2 cm" }, "solution": { "level": "PERFORMED", "subject": "Statistics", "topic": "nCr", "subTopic": "Other", "default": "\\frac{2}{m!(2-m)!}" }, "steps": { "type": "interim", "title": "$$2\\:nCr\\:m:{\\quad}\\frac{2}{m!\\left(2-m\\right)!}$$", "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 $$n=2,\\:r=m$$", "result": "=\\frac{2!}{m!\\left(2-m\\right)!}" }, { "type": "interim", "title": "Simplify $$\\frac{2!}{m!\\left(2-m\\right)!}:{\\quad}\\frac{2}{m!\\left(2-m\\right)!}$$", "input": "\\frac{2!}{m!\\left(2-m\\right)!}", "result": "=\\frac{2}{m!\\left(2-m\\right)!}", "steps": [ { "type": "interim", "title": "$$2!=2$$", "input": "2!", "steps": [ { "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" } }, { "type": "step", "result": "=\\frac{2}{m!\\left(-m+2\\right)!}" } ], "meta": { "solvingClass": "Solver" } } ] } }