{
"query": {
"display": "p(8, 4)",
"symbolab_question": "#p(8,4)"
},
"solution": {
"level": "PERFORMED",
"subject": "Statistics",
"topic": "nCr",
"subTopic": "Other",
"default": "1680"
},
"steps": {
"type": "interim",
"title": "$$8\\:nPr\\:4:{\\quad}1680$$",
"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 $$n=8,\\:r=4$$",
"result": "=\\frac{8!}{\\left(8-4\\right)!}"
},
{
"type": "interim",
"title": "$$\\frac{8!}{\\left(8-4\\right)!}=1680$$",
"input": "\\frac{8!}{\\left(8-4\\right)!}",
"result": "=1680",
"steps": [
{
"type": "step",
"primary": "Subtract the numbers: $$8-4=4$$",
"result": "=\\frac{8!}{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": [
"$$\\frac{8!}{4!}=8\\cdot\\:7\\cdot\\:6\\cdot\\:5$$"
],
"result": "=8\\cdot\\:7\\cdot\\:6\\cdot\\:5"
},
{
"type": "step",
"primary": "Refine",
"result": "=1680"
}
],
"meta": {
"solvingClass": "Solver"
}
}
]
}
}
Solution
p(8, 4)
Solution
Solution steps
Plug in
Popular Examples
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Frequently Asked Questions (FAQ)
What is p(8,4) ?
The answer to p(8,4) is 1680