Factorial Product

Number Theory Level 3

Let $N = 1!\cdot 2! \cdot 3! \cdot 4! \ldots 9! \cdot 10!$ . Let $2^k$ be the largest power of $2$ that divides $N$ . What is the value of $k$ ?

Details and assumptions

$n! = n\times (n-1) \times (n-2) \ldots 2 \times 1$ .