Question
Download Solution PDFअगर \(\rm \begin{pmatrix} 15\\ 8\end{pmatrix}+\begin{pmatrix} 15\\ 7\end{pmatrix}=\begin{pmatrix} \rm n\\ \rm r\end{pmatrix}\)
तो n और r के मान क्या हैं?
जहां, \(\begin{pmatrix} \rm n\\ \rm r\end{pmatrix} = {}^nC_r\)
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFअवधारणा:
- nCr = nCn-r
- यदि nCx = nCy तो x = y या x + y = n।
- nCr + nCr-1 = n+1Cr।
गणना:
\(\rm \begin{pmatrix} 15\\ 8\end{pmatrix}+\begin{pmatrix} 15\\ 7\end{pmatrix}=\begin{pmatrix} \rm n\\ \rm r\end{pmatrix}\)
⇒ 15C8 + 15C7 = nCr
nCr + nCr-1 = n+1Cr का उपयोग करके:
⇒ 15C8 + 15C8-1 = 15+1C8 = nCr
⇒ 16C8 = nCr
⇒ n = 16 और r = 8
Last updated on Jun 12, 2025
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