For the writing assignment, the number of ways of choosing from two essay topics three different mandatory lengths is given by:
[tex] ^2C_1 \times { ^3C_1}= 2\times3=6[/tex]
Thus, he has 20 choices to make for the writing assignment.
For the reading assignment, the number of ways of choosing from five biographies and three volumes of essays is given by:
5 x 3 = 15
Therefore, the total number of choices is given by 6 + 15 = 21 choices.