{
"query": {
"display": "5 nCr 2",
"symbolab_question": "#5 nCr 2"
},
"solution": {
"level": "PERFORMED",
"subject": "Statistics",
"topic": "nCr",
"subTopic": "Other",
"default": "10"
},
"steps": {
"type": "interim",
"title": "$$5\\:nCr\\:2:{\\quad}10$$",
"steps": [
{
"type": "definition",
"title": "Combinación",
"text": "Da el número de subconjuntos de r elementos de n elementos disponibles<br/>$$nCr=\\frac{n!}{r!\\left(n-r\\right)!}$$"
},
{
"type": "step",
"result": "=\\frac{n!}{r!\\left(n-r\\right)!}"
},
{
"type": "step",
"primary": "Sustituir $$n=5,\\:r=2$$",
"result": "=\\frac{5!}{2!\\left(5-2\\right)!}"
},
{
"type": "interim",
"title": "$$\\frac{5!}{2!\\left(5-2\\right)!}=10$$",
"input": "\\frac{5!}{2!\\left(5-2\\right)!}",
"result": "=10",
"steps": [
{
"type": "step",
"primary": "Restar: $$5-2=3$$",
"result": "=\\frac{5!}{2!\\cdot\\:3!}"
},
{
"type": "step",
"primary": "Eliminar los factoriales: $$\\frac{n!}{\\left(n-m\\right)!}=n\\cdot\\left(n-1\\right)\\cdots\\left(n-m+1\\right),\\:n>m$$",
"secondary": [
"$$\\frac{5!}{3!}=5\\cdot\\:4$$"
],
"result": "=\\frac{5\\cdot\\:4}{2!}"
},
{
"type": "step",
"primary": "Simplificar",
"result": "=\\frac{20}{2!}"
},
{
"type": "interim",
"title": "$$2!=2$$",
"input": "2!",
"steps": [
{
"type": "step",
"primary": "Aplicar las propiedades de los factoriales: $$n!=1\\cdot2\\cdot3\\cdot\\ldots\\cdot\\:n$$",
"secondary": [
"$$2!=1\\cdot\\:2$$"
],
"result": "=1\\cdot\\:2"
},
{
"type": "step",
"primary": "Multiplicar los numeros: $$1\\cdot\\:2=2$$",
"result": "=2"
}
],
"meta": {
"solvingClass": "Solver"
}
},
{
"type": "step",
"result": "=\\frac{20}{2}"
},
{
"type": "step",
"primary": "Dividir: $$\\frac{20}{2}=10$$",
"result": "=10"
}
],
"meta": {
"solvingClass": "Solver"
}
}
]
}
}
Solución
5 nCr 2
Solución
Pasos de solución
Sustituir