Add a new metric for how many times permissions prompts are shown.

chrome/browser/permissions/permission_uma_util.cc

Index: chrome/browser/permissions/permission_uma_util.cc
diff --git a/chrome/browser/permissions/permission_uma_util.cc b/chrome/browser/permissions/permission_uma_util.cc
index b27935edc4dfaba3c2b0456a1d4ac53da0a244a1..85a1360af4e10252916f5366cb32b5ae9a4be556 100644
--- a/chrome/browser/permissions/permission_uma_util.cc
+++ b/chrome/browser/permissions/permission_uma_util.cc
@@ -12,6 +12,7 @@
 #include "chrome/browser/permissions/permission_manager.h"
 #include "chrome/browser/permissions/permission_util.h"
 #include "chrome/browser/profiles/profile.h"
+#include "chrome/browser/ui/website_settings/permission_bubble_request.h"
 #include "components/rappor/rappor_service.h"
 #include "components/rappor/rappor_utils.h"
 #include "content/public/browser/permission_type.h"
@@ -274,3 +275,14 @@ void PermissionUmaUtil::PermissionRevoked(PermissionType permission,
     RecordPermissionAction(permission, REVOKED, revoked_origin);
   }
 }
+
+void PermissionUmaUtil::PermissionPromptShown(
+    const std::vector<PermissionBubbleRequest*> requests) {
+  PermissionBubbleType permission_prompt_type = PermissionBubbleType::MULTIPLE;
+  if (requests.size() == 1)
+    permission_prompt_type = requests[0]->GetPermissionBubbleType();
+  UMA_HISTOGRAM_ENUMERATION(
+      "Permissions.Prompt.Shown",
+      static_cast<base::HistogramBase::Sample>(permission_prompt_type),
+      static_cast<base::HistogramBase::Sample>(PermissionBubbleType::NUM));
+}