5 nCr 2

{ "query": { "display": "5 nCr 2", "symbolab_question": "#5 nCr 2" }, "solution": { "level": "PERFORMED", "subject": "Statistics", "topic": "nCr", "subTopic": "Other", "default": "10" }, "steps": { "type": "interim", "title": "$$5\\:nCr\\:2:{\\quad}10$$", "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 $$n=5,\\:r=2$$", "result": "=\\frac{5!}{2!\\left(5-2\\right)!}" }, { "type": "interim", "title": "$$\\frac{5!}{2!\\left(5-2\\right)!}=10$$", "input": "\\frac{5!}{2!\\left(5-2\\right)!}", "result": "=10", "steps": [ { "type": "step", "primary": "Subtract the numbers: $$5-2=3$$", "result": "=\\frac{5!}{2!\\cdot\\:3!}" }, { "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": [ "$$\\frac{5!}{3!}=5\\cdot\\:4$$" ], "result": "=\\frac{5\\cdot\\:4}{2!}" }, { "type": "step", "primary": "Refine", "result": "=\\frac{20}{2!}" }, { "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{20}{2}" }, { "type": "step", "primary": "Divide the numbers: $$\\frac{20}{2}=10$$", "result": "=10" } ], "meta": { "solvingClass": "Solver" } } ] } }