Why do we have to use octahedral voids for formula making in solid state chemistry?

Allow me to take an example to explain myself.


**Q)** What is the formula of a compound in which the element Y forms a ccp lattice and an atom of X occupy ${1\over3}$rd of tetrahedral voids?


Now to find the formula we first say that the space occupied by octahedral voids are $2$\*space occupied by tetrahedral voids = $2\over3$.


No. of atoms of element X = $2\over3$\*no. of octahedral voids
$\implies$ No. of atoms of element X = ${2\over3} \times 4$ = $8\over3$


Ratio of X and Y = ${8\over3}:4$ = $2:3$


$\therefore$ formula is $X\_2Y\_3$.


**Coming to my question -** Why can't we use space occupied by tetrahedral voids?


