<apex:page controller="AccountContactController">
 <apex:form >
<apex:pageBlock title="Account Name">
<apex:selectList value="{!selectedAccId}" size="1">
<apex:selectOptions value="{!AccountNames}" />
 </apex:selectList><br/><br/>
  <b>Related Contacts</b>
 <apex:pageblockTable title="Contacts" value="{!SelectedContacts}" var="Sc">
 <apex:column value="{!Sc.name}"/>
  <apex:column value="{!Sc.phone}"/>
 </apex:pageblockTable>
</apex:pageBlock>
</apex:form>
</apex:page>

Public with sharing class AccountContactController {
  Public Id selectedAccId{get;set;}
       List<Contact> Conlist;
       Public List<SelectOption> getAccountNames() {
              List<SelectOption> accOptions= new List<SelectOption>();
              system.debug(selectedAccId);
              accOptions.add( new SelectOption('','--Select--'));
              for(Account acc : [select Id,name from Account ] ) {
                      accOptions.add(new SelectOption(acc.Id,acc.name));
              }
             return accOptions;
       }
       Public List<Contact> getSelectedContacts(){
          Conlist=[select name,phone from Contact where Accountid=: selectedAccId];
          return Conlist;
       }
}