Writing a electrochemical cell representation in correct way
The chemical reaction is:

$$\ce{2AgCl(s) + H2(g) -&gt; 2 HCl(aq) + 2 Ag(s)}$$

If we split this into half reactions, we get an oxidation half reaction at the anode of:

$$\ce{H2(g) -&gt; 2 H+(aq) + 2 e-}$$

And a reduction half reaction at the cathode of:

$$\ce{2AgCl(s) + 2e- -&gt; 2 Ag(s) + 2 Cl-(aq)}$$

If you want all the species at standard state, you need a partial pressure of $\pu{1 bar}$ of hydrogen gas, a $\mathrm{pH}$ of about 0, and a chloride concentration of $\pu{1 mol/L}$. 

In cells where the reagents can't react directly, you don't need a salt bridge. In the reaction we are looking at, $\ce{AgCl}$ is confined to the cathode because it sticks to it, and hydrogen gas is confined to the anode because that's where we are releasing it, and it has low solubility in water.

The cell notation starts with the conductor of the anode half reaction, and ends with the conductor of the cathode half reaction. Different phases are separated by vertical lines. If there is more than one species in a phase, they are separated by commas.

$$\ce{Pt(s) | H2(g, \pu{1 bar}) |  H+(aq, \pu{1 mol/L}) , Cl- (aq, \pu{1 mol/L}) | AgCl(s) | Ag(s)}$$


  The books has plainly told 3. to be correct.


The answer is (5) none of the above. Using the format of the answer key, the best answer would be:

$$\ce{Pt(s) | H2(g), \pu{1 bar} |  1 M HCl(aq) | AgCl(s) | Ag(s)}$$

You get this answer from answer 3 by changing the salt-bridge boundary ("||") to a phase boundary ("|"). Having a salt bridge between the hydrogen gas and the aqueous hydrogen ions would mean that you are generating hydrogen ions at the electrode where they are not in contact with $\pu{1 M}$ hydrogen ions.