The number of ways of choosing triplet \( (x, y, z) \) such that \( z\max \{x, y\} \) and \( x, ...
The number of ways of choosing triplet \( (x, y, z) \) such that \( z\max \{x, y\} \) and \( x, y, z \in\{1,2, \ldots, n, n+1\} \) is
(a) \( { }^{n+1} C_{3}+{ }^{n+2} C_{3} \)
(b) \( { }^{n+1} C_{2}+2\left({ }^{n+1} C_{3}\right) \)
(c) \( 1^{2}+2^{2}+\ldots+n^{2} \)
(d) \( 2\left({ }^{n+2} C_{3}\right)-{ }^{n+1} C_{2} \)
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