Chapter 6 - Section 6.3 - Decision Algorithms: The Addition and Multiplication Principles - Exercises - Page 425: 38

$4$

The first blank (who played with (San Diego State in the first round) can be De Paul or Hofstra. If it is De Paul, the second blank (who played with Colgate in the first round) can only be Hofstra. The third blank (first in the second round) can only be De Paul, because we can see De Paul winning the tournament. The fourth blank (the second blank in the second round) is either Hofstra or Colgate. This gives 2 possibilities. If the first blank (who played with (San Diego State in the first round) is Hofstra, the second blank (who played with Colgate in the first round) can only be De Paul. The third blank (first in the second round)is either San Diego State or Hofstra. The fourth blank (the second blank in the second round) can only be De Paul, because we can see De Paul winning the tournament.. This gives 2 possibilities. Overall, there are $2+2=4$ possible ways of filling in the blanks.