The alternate code is nothing but the you specified instead of that it is one line code.

I forgot to say $option should be replaced by $value

I executed this program to my knowledge i found the following things to be change

Remove array from function definition,and keep paranthesis for $select =( $selected==$key ? " selected" : null);
...

If you got the solution then ignore this otherwise
try to update the number filed by adding 1 to it where name will be equal to the selected name from database.