Question
Download Solution PDFIf \(\rm \begin{pmatrix} 15\\ 8\end{pmatrix}+\begin{pmatrix} 15\\ 7\end{pmatrix}=\begin{pmatrix} \rm n\\ \rm r\end{pmatrix}\)
then the values of n and r are:
Where, \(\begin{pmatrix} \rm n\\ \rm r\end{pmatrix} = {}^nC_r\)
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
- nCr = nCn-r.
- If nCx = nCy, then x = y or x + y = n.
- nCr + nCr-1 = n+1Cr.
Calculations:
\(\rm \begin{pmatrix} 15\\ 8\end{pmatrix}+\begin{pmatrix} 15\\ 7\end{pmatrix}=\begin{pmatrix} \rm n\\ \rm r\end{pmatrix}\)
⇒ 15C8 + 15C7 = nCr
Using nCr + nCr-1 = n+1Cr:
⇒ 15C8 + 15C8-1 = 15+1C8 = nCr
⇒ 16C8 = nCr
⇒ n = 16 and r = 8.
Last updated on Jun 12, 2025
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