The random closed packing fraction of hard balls of three different sizes were measured by use of the Archimedes method. This packing fraction increases as the kind of balls with different sizes increases. The packing fraction is related to the mixing entropy of an ideal solution in respect to the holes among the hard balls. The composition zone of La-Al-Ni amorphous alloy made by cooling the alloy melt with a cooling rate of 90 Ks-1 is located at same zone of the largest values of packing fraction and mixing entropy of hard balls in the ternary system. where the proportion of atom sizes of La, Al and Ni is similar to that of hard balls. The packing fraction and the mixing entropy are qualitatively considered as one of the criteria of the glass forming ability of alloys The random closed packing fraction of hard balls of three different sizes were measured by use of the Archimedes method. This packing fraction increases as the kind of balls with different sizes increases. The packing fraction is related to the mixing entropy of an ideal solution in respect to the holes among the hard balls. The composition zone of La-Al-Ni amorphous alloy made by cooling the alloy melt with a cooling rate of 90 Ks-1 is located at same zone of the largest value of packing fraction and mixing entropy of where the proportion of an atom sizes of La, Al and Ni is similar to that of hard balls. The packing fraction and the mixing entropy are qualitatively considered as one of the criteria of the glass forming ability of alloys