Question 118
Let's examine all the possible sequences $a_1, a_2, ..., a_{2008}$ of non-negative integers where $a_1 \le a_2 \le ... \le a_{2008}$ and $a_k \le (k-1)$ for all values of $k$ from $1$ to $2008$. Prove that the number of such sequences exceeds
a) $2^{2007}$;
b) $2^{2008}$.
a) $2^{2007}$;
b) $2^{2008}$.