(a) How many ways can three balls of different colors - yellow, red, and green - be put in a ball can? (b) How many different one-to-one correspondences are there between the two sets {1,2,3} and {y,r,g}? (c) Explain why a dozen dyed eggs, all of different colors, can be placed in a carton in 1211109x8x7654321 ways. (d) How many different one-to-one correspondences are there between the two sets {1,2,3,..., 12} and {A,B,C,D,E,F,G,H,I,J,K,L}? (a) There are ways that the three balls can be placed in the ball can.