Determine the number of atoms in a mole of $\mathrm{Ca}{\left(\mathrm{OH}\right)}_2$?

One mole of any substance has Avogadro number of atoms, ions or molecules. This number is $6.02\times {10}^{23}$.

To calculate the total number of atoms in a mole, first figure out how many atoms make up one mole of calcium hydroxide. Then multiply that amount by the Avogadro number.

Each molecule of $\mathrm{Ca}{\left(\mathrm{OH}\right)}_2$ has a total of five atoms, one of calcium, two of oxygen and two of hydrogen.

Each atom of $\mathrm{Ca}{\left(\mathrm{OH}\right)}_2$ has $6.02\times {10}^{23}$ atoms per mole. 

 A mole of calcium hydroxide has $5\times 6.02\times {10}^{23}$atoms.

Hence option (B) is correct.