10 nPr 6

{ "query": { "display": "10 nPr 6", "symbolab_question": "#10 nPr 6" }, "solution": { "level": "PERFORMED", "subject": "Statistics", "topic": "nCr", "subTopic": "Other", "default": "151200" }, "steps": { "type": "interim", "title": "$$10\\:nPr\\:6:{\\quad}151200$$", "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 $$n=10,\\:r=6$$", "result": "=\\frac{10!}{\\left(10-6\\right)!}" }, { "type": "interim", "title": "$$\\frac{10!}{\\left(10-6\\right)!}=151200$$", "input": "\\frac{10!}{\\left(10-6\\right)!}", "result": "=151200", "steps": [ { "type": "step", "primary": "Subtract the numbers: $$10-6=4$$", "result": "=\\frac{10!}{4!}" }, { "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": [ "$$\\frac{10!}{4!}=10\\cdot\\:9\\cdot\\:8\\cdot\\:7\\cdot\\:6\\cdot\\:5$$" ], "result": "=10\\cdot\\:9\\cdot\\:8\\cdot\\:7\\cdot\\:6\\cdot\\:5" }, { "type": "step", "primary": "Refine", "result": "=151200" } ], "meta": { "solvingClass": "Solver" } } ] } }