In a class of $80$ students, $45$ play cricket, $35$ play football, and $15$ play both cricket and football. How many students play only cricket?

We can find the number of students playing only cricket using set theory properties or a Venn diagram representation.
Given:

* Total students playing cricket, $n(C)=45$
* Total students playing football, $n(F)=35$
* Students playing both sports, $n(C\cap F)=15$

The number of students who play only cricket is given by subtracting the overlapping region (both sports) from the total cricket players:

$$\text{Students playing only cricket}=n(C)-n(C\cap F)$$

$$\text{Students playing only cricket}=45-15=30$$