{
"query": {
"display": "P(12, 9)",
"symbolab_question": "#P(12,9)"
},
"solution": {
"level": "PERFORMED",
"subject": "Statistics",
"topic": "nCr",
"subTopic": "Other",
"default": "79833600"
},
"steps": {
"type": "interim",
"title": "$$12\\:nPr\\:9:{\\quad}79833600$$",
"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 $$n=12,\\:r=9$$",
"result": "=\\frac{12!}{\\left(12-9\\right)!}"
},
{
"type": "interim",
"title": "$$\\frac{12!}{\\left(12-9\\right)!}=79833600$$",
"input": "\\frac{12!}{\\left(12-9\\right)!}",
"result": "=79833600",
"steps": [
{
"type": "step",
"primary": "Subtract the numbers: $$12-9=3$$",
"result": "=\\frac{12!}{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": [
"$$\\frac{12!}{3!}=12\\cdot\\:11\\cdot\\:10\\cdot\\:9\\cdot\\:8\\cdot\\:7\\cdot\\:6\\cdot\\:5\\cdot\\:4$$"
],
"result": "=12\\cdot\\:11\\cdot\\:10\\cdot\\:9\\cdot\\:8\\cdot\\:7\\cdot\\:6\\cdot\\:5\\cdot\\:4"
},
{
"type": "step",
"primary": "Refine",
"result": "=79833600"
}
],
"meta": {
"solvingClass": "Solver"
}
}
]
}
}
Solution
P(12, 9)
Solution
Solution steps
Plug in
Popular Examples
thirdquartile 9.4,48.4,35.4,37,29,31,64.4,37.4,16.6,28.6upper quartile arithmeticmean of 2,4,4,5,6,6,7,8,12average median of 3,5,2,1,4median 10 nPr 6variance of-25,2,3,3,8,10,12,14,18,21,21variance
Frequently Asked Questions (FAQ)
What is P(12,9) ?
The answer to P(12,9) is 79833600