Discussion
Consider a BIBD with parameter \((v, b, r, k, \lambda)\). If \(v = b = 11\) and \(r = 5\), then :
Answer: A
The parameters are \(k = 5, \lambda = 2\).
For a BIBD, \(bk = vr\) and \(\lambda(v - 1) = r(k - 1)\). With \(v = b = 11\) and \(r = 5\):
\[ \begin{aligned} 11k &= 11 \cdot 5 \Rightarrow k = 5 \\ 10\lambda &= 5 \cdot 4 \Rightarrow \lambda = 2 \end{aligned} \]
(A symmetric design has \(k = r\).) \(\lambda = 1\) would need \(10 = 20\), and \(k = 2\) or \(k = 11\) contradicts \(bk = vr\).
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