How to create a rule to send an email to a list of selected email addresses?
Assuming this question is about D7, you can use the Rules module to create a rule like so (in Rules export format):

{ "rules_send_email_to_selected_email_ids" : {
    "LABEL" : "Send eMail to selected eMail IDs",
    "PLUGIN" : "reaction rule",
    "OWNER" : "rules",
    "REQUIRES" : [ "rules" ],
    "ON" : {
      "node_insert--article" : { "bundle" : "article" }
    },
    "DO" : [
      { "LOOP" : {
          "USING" : { "list" : [ "node:field-email-addresses" ] },
          "ITEM" : { "current_email_id" : "Current eMail ID" },
          "DO" : [
            { "drupal_message" : { "message" : "An eMail about this new content with title \u0022[node:title]\u0022 and URL [node:url] will be delivered to [current-email-id:value]." } },
            { "mail" : {
                "to" : "[current-email-id:value]",
                "subject" : "You have new mail ...",
                "message" : "New content was created with title [node:title] ... You can read about it at [node:url].",
                "language" : [ "" ]
              }
            }
          ]
        }
      }
    ]
  }
}


Some more details about the above rule:


Rules Event: After saving new content of type "Article" (adapt the type to fit your needs, ie to XYZ).
Rules Action: a "loop" for all selected values of a multi value select list (contain the eMail IDs), with machine name field_email_addresses (adapt the machine name to fit your needs). For each item (= current_email_id), an eMail is created with some subject and message that also contains the title and url of the node being created. Note: this will send 1 separated eMail to each of the selected eMail IDs (there is no way to send a single eMail to all selected eMail IDs).


If you have the Rules UI enabled, you can import the above rule in your own site, after you adapt the machine names of the content type and the field name containing the list of eMail Ids.

After you're convinced the rule works as expected, you may want to remove the Rules Action that displays a message after the node is saved (with drupal_message).

Video tutorial: have a look at the List and loops video which show a similar scenario.