We are dealing with a problem related to set theory. Let's denote:

• $B$ as the set of students who like basketball ($|B| = 22$),
• $T$ as the set of students who like tennis ($|T| = 18$),
• $V$ as the set of students who like volleyball ($|V| = 14$),
• $|T \cap V| = 7$ (students who like both tennis and volleyball),
• $|B \cap T \cap V| = 3$ (students who like all three sports).

The goal is typically to find the number of students who like only one sport or combinations of two sports. Let's solve the problem systematically.

1. Three-sport intersection:
   The number of students who like all three sports ($B \cap T \cap V$) is already given as 3.

2. Tennis and Volleyball intersection but not Basketball:
   The number of students who like both tennis and volleyball but not basketball can be calculated by subtracting the 3 who like all three sports from the 7 who like both tennis and volleyball: $|T \cap V| - |B \cap T \cap V| = 7 - 3 = 4$ So, 4 students like only tennis and volleyball.

3. Finding the remaining sets:
   To find the number of students who like only one sport or exactly two sports, we would need more information about the overlaps between basketball and the other two sports (i.e., $B \cap T$, $B \cap V$) or we can make assumptions if this information is unavailable.

Would you like to continue solving this with additional assumptions or clarifications?

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Related Questions:

1. How many students like only basketball?
2. How many students like basketball and tennis but not volleyball?
3. What is the total number of students who like only one sport?
4. How many students like volleyball but not tennis or basketball?
5. What is the total number of students who like at least two sports?

Tip: Visualizing with a Venn diagram can greatly help with understanding intersections and unique counts in set problems.