Solution
= Solution
Each unordered triple of <vertices> is a <triangle in a graph> with probability $p^3$. Consequently the <triangle count in a binomial random graph> satisfies $\mathbb E X=\binom n3p^3\leq(np)^3/6$. If $np\to0$, the <Markov inequality> gives $\mathbb P(X>0)\leq\mathbb E X\to0$. Hence
$$
\boxed{\mathbb P(X=0)\longrightarrow1},
$$
the sparse direction of the <triangle-existence threshold in a binomial random graph>.