Chapter 7 - Section 7.4 - The Binomial Theorem - 7.4 Exercises - Page 664: 20

$1$

The binomial coefficient can be expressed as: $$_nC_k=\dfrac{n!}{(n-k)! \ k!}$$ Substitute $4$ for $n$ and $0$ for $k$ in the above formula. Therefore, $$_4C_0=\dfrac{4!}{0! \ (4-0)!} \\ =\dfrac{4!}{1\cdot 4!}\\=\dfrac{ 4 !}{4 !}\\= 1 $$