A children's toy truck-carrier is formed by a trailer and ten small cars transported on it. In the production sector of the company that manufactures this toy, all the small cars are painted so that the toy looks more attractive. The colors used are yellow, white, orange and green, and each small car is painted with only one color. The truck-carrier has a fixed color. The company determined that in every truck-carrier there must be at least one small car of each of the four available colors. Change of position of the small cars on the truck-carrier does not generate a new model of the toy. Based on this information, how many distinct models of the truck-carrier toy can this company produce? (A) $C_{6,4}$ (B) $C_{9,3}$ (C) $C_{10,4}$ (D) $6^{4}$ (E) $4^{6}$
A children's toy truck-carrier is formed by a trailer and ten small cars transported on it. In the production sector of the company that manufactures this toy, all the small cars are painted so that the toy looks more attractive. The colors used are yellow, white, orange and green, and each small car is painted with only one color. The truck-carrier has a fixed color. The company determined that in every truck-carrier there must be at least one small car of each of the four available colors. Change of position of the small cars on the truck-carrier does not generate a new model of the toy.
Based on this information, how many distinct models of the truck-carrier toy can this company produce?\\
(A) $C_{6,4}$\\
(B) $C_{9,3}$\\
(C) $C_{10,4}$\\
(D) $6^{4}$\\
(E) $4^{6}$