Doubt from solid state

A crystal is made of particles X, Y and Z. X forms FCC packing. Y occupies all the octahedral void of X and Z all the tetrahedral voids of X. If all the particle along one body diagonal are removed then the formula for the crystal would be.

Ans: X5Y4Z8

Initially
X= 4
Y=4
Z=8
Finally
X=4-1/4 = 15/4
Y=4-1=3
Z= 8-2 =6
Therefore X:Y:Z = 5:4:8

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