Solve the following problems and be sure to show all your work. (a) what is the coefficient on x 57y 43 in the expansion of (x + y) 100? do not simplify your answer. (b) what is the coefficient on x 57y 43 in the expansion of (−x − 3y) 100? do not simplify your answer. (c) in the expansion of (x + y) 100, is there a term whose only x and y components are x 58y 43? why or why not? (d) how many possible distinct rearrangements of the letters spaceship are there? do not simplify your answer. hint: any two of the same letter are indistinguishable from one another. for example, the two ps are indistinguishable.