{
"query": {
"display": "C(145, 9)",
"symbolab_question": "#C(145,9)"
},
"solution": {
"level": "PERFORMED",
"subject": "Statistics",
"topic": "nCr",
"subTopic": "Other",
"default": "\\frac{2.19946E19}{362880}"
},
"steps": {
"type": "interim",
"title": "$$145\\:nCr\\:9:{\\quad}\\frac{2.19946E19}{362880}$$",
"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 $$n=145,\\:r=9$$",
"result": "=\\frac{145!}{9!\\left(145-9\\right)!}"
},
{
"type": "interim",
"title": "$$\\frac{145!}{9!\\left(145-9\\right)!}=\\frac{2.19946E19}{362880}$$",
"input": "\\frac{145!}{9!\\left(145-9\\right)!}",
"result": "=\\frac{2.19946E19}{362880}",
"steps": [
{
"type": "step",
"primary": "Subtract the numbers: $$145-9=136$$",
"result": "=\\frac{145!}{9!\\cdot\\:136!}"
},
{
"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": [
"$$\\frac{145!}{136!}=145\\cdot\\:144\\cdot\\:143\\cdot\\:142\\cdot\\:141\\cdot\\:140\\cdot\\:139\\cdot\\:138\\cdot\\:137$$"
],
"result": "=\\frac{145\\cdot\\:144\\cdot\\:143\\cdot\\:142\\cdot\\:141\\cdot\\:140\\cdot\\:139\\cdot\\:138\\cdot\\:137}{9!}"
},
{
"type": "step",
"primary": "Refine",
"result": "=\\frac{2.19946E19}{9!}"
},
{
"type": "interim",
"title": "$$9!=362880$$",
"input": "9!",
"steps": [
{
"type": "step",
"primary": "Apply factorial rule: $$n!=1\\cdot2\\cdot3\\cdot\\ldots\\cdot\\:n$$",
"secondary": [
"$$9!=1\\cdot\\:2\\cdot\\:3\\cdot\\:4\\cdot\\:5\\cdot\\:6\\cdot\\:7\\cdot\\:8\\cdot\\:9$$"
],
"result": "=1\\cdot\\:2\\cdot\\:3\\cdot\\:4\\cdot\\:5\\cdot\\:6\\cdot\\:7\\cdot\\:8\\cdot\\:9"
},
{
"type": "step",
"primary": "Multiply the numbers: $$1\\cdot\\:2\\cdot\\:3\\cdot\\:4\\cdot\\:5\\cdot\\:6\\cdot\\:7\\cdot\\:8\\cdot\\:9=362880$$",
"result": "=362880"
}
],
"meta": {
"solvingClass": "Solver"
}
},
{
"type": "step",
"result": "=\\frac{2.19946E19}{362880}"
}
],
"meta": {
"solvingClass": "Solver"
}
}
]
}
}
Solution
C(145, 9)
Solution
Solution steps
Plug in
Popular Examples
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Frequently Asked Questions (FAQ)
What is C(145,9) ?
The answer to C(145,9) is (2.19946E19)/(362880)