The land of Catania uses gold coins and silver coins. Gold coins are 1 mm thick and silver coins are 3 mm thick. In how many ways can Taylor make a stack of coins that is 8 mm tall using any arrangement of gold and silver coins, assuming order matters?
(A)3(B)7(C)10(D)13(E)16
Let g and s be the numbers of gold and silver coins, respectively.g+3s=8s012g852
Case 1: s=0,g=8⟹1 case.
Case 2: s=1,g=5⟹sggggg⟹(16)=6 cases ((16) ways to determine the position of s and the rest have to be g)