Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

$https://latex.codecogs.com/png.image?\dpi{150}\\\text{Als je }\: V_{n}^{p}\\\text{deelt door }\\\text{ }\; \; V_{n-1}^{p-1}\\\text{verkrijg je}$	A. $\boldsymbol{n }$
	B. $\boldsymbol{n-1}$
	C. $\large\boldsymbol{\frac pn }$
	D. $\large\boldsymbol{\frac {1} {n\,-\,1} }$
	E. $\large\boldsymbol{\frac 1n }$

[ 5-2873 - op net sinds 30.3.13-()-24.11.2024 ]

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Oplossing - Solution

$https://latex.codecogs.com/png.image?\dpi{110}\frac{V_{n}^{p}}{V_{n-1}^{p-1}}=\frac{\frac{n!}{(n-p)!}}{\frac{(n-1)!}{\left [ (n-1)-(p-1) \right ]!}}=\frac{n!}{(n\!-\!p)!} \cdot \frac{(n\!-\!p)!}{(n\!-\!1)!}=\frac{n!}{(n\!-\!1)!}=n$

$https://latex.codecogs.com/png.image?\dpi{150}\\\text{Als je }\: V_{n}^{p}\\\text{deelt door }\\\text{ }\; \; V_{n-1}^{p-1}\\\text{verkrijg je}$	A. \(\boldsymbol{n }\)
	B. \(\boldsymbol{n-1}\)
	C. \(\large\boldsymbol{\frac pn }\)
	D. \(\large\boldsymbol{\frac {1} {n\,-\,1} }\)
	E. \(\large\boldsymbol{\frac 1n }\)