Which AWS service can the company use to allow customers to sign into its online store using social media or other external identity providers?

Amazon Cognito is the correct choice because it provides identity management for web and mobile applications, enabling user sign-up, sign-in, and access control. It supports federation with social identity providers (like Facebook, Google, Apple) and enterprise identity providers. AWS Directory Service is for integrating AWS with on-premises directories or setting up managed directories in the cloud, not for customer-facing application authentication. AWS Identity and Access Management (IAM) is for managing access to AWS resources for AWS users and services, not for application end-users. AWS IAM Identity Center (AWS Single Sign-On) centralizes access management to multiple AWS accounts and business applications for your workforce, not for external customers of an online store.