With reference to Exercise 1.1, suppose that there is a third step, and if the first step is made in the ith way and the second step in the jth way, the third step can be made in n3ij ways.

(a) Use a tree diagram to verify that the whole operation can be made in

Different ways.

(b) With reference to part (b) of Exercise 1.1, use the formula of part (a) to verify that there are 32 ways in which the student can study at most 4 hours for the test on three consecutive days.

i=1 j=1 %3D1 3D1