The correct option for the number of body centred unit cells in all 14 types of Bravais lattice unit cells is :

To determine the number of body-centered unit cells among all the 14 types of Bravais lattices, we can analyze the distribution of lattice types across the 7 crystal systems.

The 14 Bravais lattices are categorized under 7 crystal systems as follows:
1. Cubic system: Primitive, Body-centered, Face-centered (3 lattices)
2. Tetragonal system: Primitive, Body-centered (2 lattices)
3. Orthorhombic system: Primitive, Body-centered, Face-centered, End-centered (4 lattices)
4. Hexagonal system: Primitive (1 lattice)
5. Rhombohedral (Trigonal) system: Primitive (1 lattice)
6. Monoclinic system: Primitive, End-centered (2 lattices)
7. Triclinic system: Primitive (1 lattice)

From the list above, we can identify which crystal systems possess a body-centered (I) unit cell:
- Cubic system has a body-centered unit cell.
- Tetragonal system has a body-centered unit cell.
- Orthorhombic system has a body-centered unit cell.

No other crystal system has a body-centered lattice. Adding these up:
$1\text{(Cubic)}+1\text{(Tetragonal)}+1\text{(Orthorhombic)}=3$

Therefore, the total number of body-centered unit cells in all 14 types of Bravais lattices is 3.