7p5

{ "query": { "display": "7p5", "symbolab_question": "#7p5" }, "solution": { "level": "PERFORMED", "subject": "Statistics", "topic": "nCr", "subTopic": "Other", "default": "2520" }, "steps": { "type": "interim", "title": "$$7\\:nPr\\:5:{\\quad}2520$$", "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 $$n=7,\\:r=5$$", "result": "=\\frac{7!}{\\left(7-5\\right)!}" }, { "type": "interim", "title": "$$\\frac{7!}{\\left(7-5\\right)!}=2520$$", "input": "\\frac{7!}{\\left(7-5\\right)!}", "result": "=2520", "steps": [ { "type": "step", "primary": "Subtract the numbers: $$7-5=2$$", "result": "=\\frac{7!}{2!}" }, { "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": [ "$$\\frac{7!}{2!}=7\\cdot\\:6\\cdot\\:5\\cdot\\:4\\cdot\\:3$$" ], "result": "=7\\cdot\\:6\\cdot\\:5\\cdot\\:4\\cdot\\:3" }, { "type": "step", "primary": "Refine", "result": "=2520" } ], "meta": { "solvingClass": "Solver" } } ] } }