{
"query": {
"display": "4nCr 2",
"symbolab_question": "#4nCr 2"
},
"solution": {
"level": "PERFORMED",
"subject": "Statistics",
"topic": "nCr",
"subTopic": "Other",
"default": "6"
},
"steps": {
"type": "interim",
"title": "$$4\\:nCr\\:2:{\\quad}6$$",
"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 $$n=4,\\:r=2$$",
"result": "=\\frac{4!}{2!\\left(4-2\\right)!}"
},
{
"type": "interim",
"title": "$$\\frac{4!}{2!\\left(4-2\\right)!}=6$$",
"input": "\\frac{4!}{2!\\left(4-2\\right)!}",
"result": "=6",
"steps": [
{
"type": "step",
"primary": "Restar: $$4-2=2$$",
"result": "=\\frac{4!}{2!\\cdot\\:2!}"
},
{
"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": [
"$$\\frac{4!}{2!}=4\\cdot\\:3$$"
],
"result": "=\\frac{4\\cdot\\:3}{2!}"
},
{
"type": "step",
"primary": "Simplificar",
"result": "=\\frac{12}{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{12}{2}"
},
{
"type": "step",
"primary": "Dividir: $$\\frac{12}{2}=6$$",
"result": "=6"
}
],
"meta": {
"solvingClass": "Solver"
}
}
]
}
}
Solución
4nCr 2
Solución
Pasos de solución
Sustituir