Explain why the following two problems are identical and solve them.
(a) In how many ways can 12 balls be placed in 3 boxes, when the first box can hold 3 balls, the second box can hold 4 balls, and the third box can hold 5 balls.
(b) In how many ways can 3 red balls, 4 blue balls, and 5 green balls be placed in a straight line?
(see Problem 1.7.14)