PageBlockTable is not getting refreshed

Question

I have an account list when user selects an account its related contacts should come in pageblocktable.

public class assignment1 
{
public Account acc{get;set;}
public List<wrap> wrapList{get;set;}
public List<SelectOption> allAccounts{get;set;}

public assignment1()
{
    acc = new Account();
    wrapList = new List<wrap>();
    allAccounts = new List<SelectOption>();
    getAddAccounts();
}

public void getAddAccounts()
{
    List<Account> accList =[Select id, name From Account];
    for(Account acc : accList)
    {
        allAccounts.add(new SelectOption(acc.id, acc.name));
    }
}

public void search()
{
    wrapList.clear();
    for(Contact con : [Select id, name, firstname, lastname, email, Email_Sent__c From Contact where accountId =: acc.id])
    {
        wrapList.add(new wrap(con));
    }
}

public void sendEmail()
{
    List<String> emailList = new List<String>();
    for(wrap w : wrapList)
    {
        if(w.checkBox == true)
        {
            if(w.con.email != null)
            {
                emailList.add(w.con.email);
            }
        }
    }
        Messaging.singleEmailMessage msg = new Messaging.singleEmailMessage();
        msg.toAddresses = emailList;
        msg.subject = 'hello';
        msg.plainTextBody ='Hi there !!!!';
        List<Messaging.sendEmailResult> r = Messaging.sendEmail(new List<Messaging.singleEmailMessage>{msg});
}

public class wrap
{
    public contact con{get;set;}
    public boolean checkBox{get;set;}
    public wrap(Contact con)
    {
        this.con = con;
        checkBox = false;
    }
}
}

Visualforce Page

<apex:page controller="assignment1">
<apex:form >
    <apex:pageBlock >
        <apex:actionRegion >
            <apex:selectList value="{!acc}" size="1"> 
                <apex:selectOptions value="{!allAccounts}" />
                <apex:actionSupport rerender="pbs" action="{!search}"/>
            </apex:selectList>
        </apex:actionRegion>
        <apex:outputPanel id="pbs">
            <apex:pageBlockSection >
                <apex:pageBlockTable var="row" value="{!wrapList}">
                    <apex:column headerValue="Action">
                        <apex:inputCheckbox value="{!row.checkBox}"/>
                    </apex:column>
                    <apex:column value="{!row.con.firstname}"/>
                    <apex:column value="{!row.con.lastname}"/>
                    <apex:column value="{!row.con.email}"/>
                    <apex:column value="{!row.con.Email_Sent__c}"/>
                </apex:pageBlockTable>
            </apex:pageBlockSection>
        </apex:outputPanel>
        <apex:commandButton action="{!sendEmail}" value="Send Email"/>
    </apex:pageBlock>
</apex:form>
</apex:page>

Answer 1

public Account acc{get;set;}

into

public Id acc{get;set;}

Change its type to string and then in your query instead of acc.Id use acc.

Because a select list always give us string and in your case you are binding it with account instance.

Also add a event="onchange" in your actionsupport tag.

Answer 2

You need to change

public Account acc{get;set;} 

to

public String acc{get;set;}

Remove the line acc = new Account(); in constructor.

And in the SOQL query needs to be changed to

Select id, name, firstname, lastname, email, Email_Sent__c From Contact where accountId =: acc

Plus add a event attribute in apex:actionSupport to make the apex call when someone changes the select list selection

<apex:actionSupport event="onchange" rerender="pbs" action="{!search}"/>