This is code snippet how you can achieve this with the help of RadioGroups
Your dialog layout should look like this :- 
<LinearLayout xmlns:android="http://schemas.android.com/apk/res/android"
    xmlns:tools="http://schemas.android.com/tools"
    android:layout_width="match_parent"
    android:layout_height="match_parent"
    android:orientation="vertical"
    tools:context="com.example.test.MainActivity" >
    <TextView
        android:id="@+id/headerTxt"
        android:layout_width="match_parent"
        android:layout_height="wrap_content"
        android:layout_gravity="center_horizontal"
        android:background="#ff669900"
        android:gravity="center_horizontal"
        android:padding="5dp"
        android:text="Pick Service"
        android:textColor="#FFF"
        android:textSize="20sp" />
    <RelativeLayout
        android:layout_width="wrap_content"
        android:layout_height="wrap_content"
        android:layout_below="@+id/textView1"
        android:layout_margin="10dp"
        android:layout_marginTop="32dp" >
        <RelativeLayout
            android:layout_width="wrap_content"
            android:layout_height="wrap_content" >
            <TextView
                android:id="@+id/primaryTxt"
                android:layout_width="wrap_content"
                android:layout_height="wrap_content"
                android:layout_alignParentLeft="true"
                android:checked="true"
                android:text="Primary Service"
                android:textSize="18sp" />
            <TextView
                android:id="@+id/primaryContentTxt"
                android:layout_width="wrap_content"
                android:layout_height="wrap_content"
                android:layout_alignParentLeft="true"
                android:layout_below="@+id/primaryTxt"
                android:text=" -Dusting \n -Sweeping \n -Washing \n -Cleaning " />
            <RadioGroup
                android:id="@+id/radioGroup1"
                android:layout_width="wrap_content"
                android:layout_height="wrap_content"
                android:layout_alignParentRight="true"
                android:layout_alignParentTop="true" >
                <RadioButton
                    android:id="@+id/service_1"
                    android:layout_width="wrap_content"
                    android:layout_height="wrap_content"
                     />
                <RadioButton
                    android:id="@+id/service_2"
                    android:layout_width="wrap_content"
                    android:layout_height="wrap_content"
                    android:layout_marginTop="50dp" />
            </RadioGroup>
            <TextView
                android:id="@+id/otherTxt"
                android:layout_width="wrap_content"
                android:layout_height="wrap_content"
                android:layout_below="@+id/primaryContentTxt"
                android:layout_marginTop="10dp"
                android:checked="true"
                android:gravity="left"
                android:text="Other Service(Soon)"
                android:textSize="18sp" />
        </RelativeLayout>
    </RelativeLayout>
    <LinearLayout
        android:id="@+id/closeLyt"
        android:layout_width="match_parent"
        android:layout_height="wrap_content"
        android:background="@android:color/darker_gray"
        android:weightSum="2" >
        <TextView
            android:id="@+id/cancelTxt"
            android:layout_width="0dp"
            android:layout_height="wrap_content"
            android:layout_gravity="center"
            android:layout_margin="1dp"
            android:layout_weight="1"
            android:background="#fff"
            android:gravity="center"
            android:padding="5dp"
            android:text="CANCEL"
            android:textColor="#000"
            android:textSize="20sp" />
        <TextView
            android:id="@+id/okTxt"
            android:layout_width="0dp"
            android:layout_height="wrap_content"
            android:layout_gravity="center"
            android:layout_margin="1dp"
            android:layout_weight="1"
            android:background="#fff"
            android:gravity="center"
            android:padding="5dp"
            android:text="OK"
            android:textColor="#000"
            android:textSize="20sp" />
    </LinearLayout>
</LinearLayout>
And you can inflate this layout in custom dialog box and with the help of radio buttons you can choose service type
int serviceNumber = 0;
    void OpenDialogService() {
        final Dialog dialog = new Dialog(this);
        dialog.getWindow();
        dialog.requestWindowFeature(Window.FEATURE_NO_TITLE);
        dialog.setContentView(R.layout.pop_new_order2);
        dialog.setCancelable(true);
        dialog.setCanceledOnTouchOutside(true);
        TextView headerTxt = (TextView) dialog.findViewById(R.id.headerTxt);
        TextView okTxt = (TextView) dialog.findViewById(R.id.okTxt);
        TextView cancelTxt = (TextView) dialog.findViewById(R.id.cancelTxt);
        TextView primaryTxt = (TextView) dialog.findViewById(R.id.primaryTxt);
        TextView otherTxt = (TextView) dialog.findViewById(R.id.otherTxt);
        TextView primaryContentTxt = (TextView) dialog.findViewById(R.id.primaryContentTxt);
        LinearLayout closeLyt = (LinearLayout) dialog.findViewById(R.id.closeLyt);
        // Radio Buttons
        final RadioGroup radio = (RadioGroup) dialog.findViewById(R.id.radioGroup1);
        radio.setOnCheckedChangeListener(new OnCheckedChangeListener() {
            @Override
            public void onCheckedChanged(RadioGroup group, int checkedId) {
                  View radioButton = radio.findViewById(checkedId);
                    int index = radio.indexOfChild(radioButton);
                    Toast.makeText(getApplicationContext(), "service" +index, 500).show();
                    serviceNumber = index+1;
            }
        });
        headerTxt.setText("Pick Services");
        //TODO change color here
        // headerTxt.setBackgroundResource(R.drawable.bg_dialog_header_success);
        // closeLyt.setBackgroundResource(R.color.selector_close_alert_dialog_success);
        closeLyt.setOnClickListener(new OnClickListener() {
            @Override
            public void onClick(View v) {
                dialog.dismiss();
            }
        });
        cancelTxt.setOnClickListener(new OnClickListener() {
            @Override
            public void onClick(View v) {
                dialog.dismiss();
            }
        });
        okTxt.setOnClickListener(new OnClickListener() {
            @Override
            public void onClick(View v) {
                dialog.dismiss();
                Bundle b = getIntent().getExtras();
                if (b == null)
                    b = new Bundle();
                b.putString("service_id", String.valueOf(serviceNumber));
                Toast.makeText(getApplicationContext(), "service " + String.valueOf(serviceNumber), 500).show();
                //TODO Handle Activity Transition Here
                // startActivity(new Intent(MainActivity.this,
                // Step1.class).addFlags(Intent.FLAG_ACTIVITY_CLEAR_TOP).putExtras(b));
                // overridePendingTransition(R.anim.push_left_in,
                // R.anim.push_left_out);
            }
        });
        dialog.show();
    }
Result
