The exponent of $$11$$ in the prime factorization of $$300!$$ is

Let $${x_n}$$ denote the number of binary strings of length $$n$$ that contains no consecutive $$0s$$.

Which of the following recurrences does $${x_n}$$ satisfy?

Let $${x_n}$$ denote the number of binary strings of length $$n$$ that contain no consecutive $$0s$$.

The value of $${x_5}$$ is

What is the chromatic number of the following graph?