In a survey of students about favorite sports, the results include 25 who like tennis, 28 who like football, 7 who like tennis and football, 20 who like tennis and baseball, 24 who like football and baseball, 5 who like all three sports, and 9 who like none of the sports. How many students like only tennis and football? How many students like only tennis and baseball? How many students like only baseball and football?
To solve this problem, we can use the principle of inclusion-exclusion. Let's denote the number of students who like only tennis as $x$, the number of students who like only football as $y$, and the number of students who like only baseball as $z$.
We know that $25$ students like tennis, $28$ like football, and $5$ like all three sports. Thus, the number of students who like only tennis can be represented as $25 - 7 - x$ (subtracting the students who also like football and the students who like all three sports). Similarly, the number of students who like only football can be represented as $28 - 7 - y$, and the number of students who like only baseball can be represented as $z - 5$.
We also know that $20$ students like tennis and baseball, and $24$ like football and baseball. Therefore, we have the following equations:
$(25 - 7 - x) + (20 - 5) + (x + y + 5) + (24 - 5) + (28 - 7 - y) + (9) = 100$
Simplifying, we get:
$(43 - x - y) + (15) + (29) = 100$
$87 - x - y = 100$
$x + y = 13$
We can now substitute this value into one of our original equations and solve for the number of students who like only tennis and football. Let's substitute into the equation for students who like only tennis:
$25 - 7 - x = x$
$18 = 2x$
$x = 9$
Therefore, $9$ students like only tennis and $4$ students like only football.
Now, let's calculate the number of students who like only tennis and baseball. Substituting into the equation for students who like only tennis and baseball:
$20 - 5 = 9$
$15 = 9$
Therefore, $9$ students like only tennis and baseball.
Finally, let's calculate the number of students who like only baseball and football. Substituting into the equation for students who like only baseball and football:
$24 - 5 = y$
$19 = y$
Therefore, $19$ students like only baseball and football. Answer: \boxed{9, 9, 19}.