1. **State the problem:** We need to find the number of ways to arrange 20 cars in a row where the cars are distinguishable only by their colors. There are 4 blue, 3 black, 5 yellow, and 8 white cars. 2. **Formula used:** When arranging $n$ objects where there are groups of indistinguishable objects, the number of distinct permutations is given by the multinomial formula: $$\frac{n!}{n_1! \times n_2! \times \cdots \times n_k!}$$ where $n$ is the total number of objects, and $n_1, n_2, ..., n_k$ are the counts of indistinguishable objects in each group. 3. **Apply the formula:** Here, $n=20$, $n_1=4$ (blue), $n_2=3$ (black), $n_3=5$ (yellow), $n_4=8$ (white). 4. **Calculate factorials:** $$20!$$ $$4! = 24$$ $$3! = 6$$ $$5! = 120$$ $$8! = 40320$$ 5. **Write the expression:** $$\frac{20!}{4! \times 3! \times 5! \times 8!}$$ 6. **Simplify step-by-step:** First, write the denominator: $$4! \times 3! \times 5! \times 8! = 24 \times 6 \times 120 \times 40320$$ Calculate denominator: $$24 \times 6 = 144$$ $$144 \times 120 = 17280$$ $$17280 \times 40320 = 696729600$$ 7. **Calculate numerator:** $20! = 2432902008176640000$ 8. **Divide numerator by denominator:** $$\frac{2432902008176640000}{696729600} = 3491888400$$ 9. **Final answer:** There are $3491888400$ ways to arrange the cars.