Page:
<apex:page controller="picklistRenderController">
<apex:form >
    <apex:pageBlock >
        <apex:selectList value="{!selectId}" size="1">
            <apex:selectOptions value="{!display}"></apex:selectOptions>
            <apex:actionSupport event="onchange" action="{!displayButton}" reRender="buttons"/>
        </apex:selectList>
        <apex:pageBlockButtons location="bottom">
        <apex:outputPanel id="buttons">
            <apex:commandButton action="{buttonA}" value="Button A" rendered="{!Y}"/>
            <apex:commandButton action="{buttonB}" value="Button B" rendered="{!X}"/>
            </apex:outputPanel>
        </apex:pageBlockButtons>
     </apex:pageBlock>
</apex:form>
</apex:page>

class:


public class picklistRenderController
{

   public List<selectOption> display { get; set; }
   public String selectId { get; set; }
   public Boolean X { get; set; }
   public Boolean Y { get; set; }
   
    public picklistRenderController() 
    
    {
    
    
        Y=True;
        display= new List<selectOption>();
        display.add(new selectoption('none','-select-'));
        display.add(new selectoption('Show','Show'));
        display.add(new selectoption('Hide','Hide'));
    }

     public void displayButton()
     
      {
      
         
         if (selectId =='Show')
         X=True;
         else
         X=False;
                         
      }
      
     
        
    
    public PageReference buttonA()
    
     {
        return null;
        
     }
     
     
      public PageReference buttonB()
    
     {
        
        return null;
     }
}