7 choose 6

{ "query": { "display": "7C6", "symbolab_question": "#7C6" }, "solution": { "level": "PERFORMED", "subject": "Statistics", "topic": "nCr", "subTopic": "Other", "default": "7" }, "steps": { "type": "interim", "title": "$$7\\:nCr\\:6:{\\quad}7$$", "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 $$n=7,\\:r=6$$", "result": "=\\frac{7!}{6!\\left(7-6\\right)!}" }, { "type": "interim", "title": "$$\\frac{7!}{6!\\left(7-6\\right)!}=7$$", "input": "\\frac{7!}{6!\\left(7-6\\right)!}", "result": "=7", "steps": [ { "type": "step", "primary": "Subtract the numbers: $$7-6=1$$", "result": "=\\frac{7!}{6!\\cdot\\:1!}" }, { "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": [ "$$\\frac{7!}{6!}=7$$" ], "result": "=\\frac{7}{1!}" }, { "type": "step", "primary": "Apply factorial rule: $$n!=1\\cdot2\\cdot3\\cdot\\ldots\\cdot\\:n$$", "secondary": [ "$$1!=1$$" ], "result": "=\\frac{7}{1}" }, { "type": "step", "primary": "Apply rule $$\\frac{a}{1}=a$$", "result": "=7" } ], "meta": { "solvingClass": "Solver" } } ] } }