अगर \(\rm \begin{pmatrix} 15\\ 8\end{pmatrix}+\begin{pmatrix} 15\\ 7\end{pmatrix}=\begin{pmatrix} \rm n\\ \rm r\end{pmatrix}\) 

तो n और r के मान क्या हैं?

जहां,  \(\begin{pmatrix} \rm n\\ \rm r\end{pmatrix} = {}^nC_r\)

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  1. 16 और 7
  2. 16 और 8
  3. 16 और 9
  4. 30 और 15

Answer (Detailed Solution Below)

Option 2 : 16 और 8
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Detailed Solution

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अवधारणा:

  • 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+1Cका उपयोग करके:

⇒ ​15C8 + 15C8-1 = 15+1C8nCr

⇒ ​16C8 = nCr

n = 16 और r = 8

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