What is a 3:1 mux? How many selection lines does it have? What is its truth table? What will be the output for the unused value in the selection line if it has a selection line which is two bits wide ?
For N select lines a MUX can have maximum of 2^N inputs. That's why you see MUXs with 2,4,8,16 inputs. When you do design using standard cell based approach you will only have 2,4,8..input MUXs. But if do design using full custom approach and you have only 3 inputs to select than you can have 3:1 MUX also. But in this case you need create layout of MUX yourself because MUXs with odd inputs are not available as a part of standard cell library.
mux ns nothing but a device that directs 2^n input lines to 1 output using select lines. generally 2^n inputs require n select lines. So thats why you can see only 4:1 8:1 mux and not odd numbers like 3:1 5:1 etc. If you connect one of the input lines say x3 (starting from x0) to 0 and use other input lines you get 3:1 mux provided you don't select the x3 line using the combination of 11 on the select line . that can be done using external logic. so to convert 4:1 mux to 3:1 mux its enough if you dont select the extra line using the select combination.
Is it possible to make a 3:1 mux with two selection line? Even if I convert at 4:1 mux to 3:1 mux the selection lines for the fourth option the ground will come as output in the way you suggested to convert a 4:1 to 3:1 mux. It is also not possible to avoid the fourt option to appear at the selectionline.
In that case, you need to avoid the 11 combination for select lines in your control logic. One other method is tie input lines 3 and 4 so that input 3 is available in output when select lines are 1X. This will increase input capacitance for input 3. This may slow down your logic. OR use 3 selection line MUX.