I agree with the suggested answer BCF. Here's a breakdown of why these options are correct and why the others are not:

Correct Options:

B: Configure a SAML identity provider in Amazon Cognito to map attributes to the Amazon Cognito user pool attributes.
- Reasoning: Cognito User Pools allow federation with SAML identity providers. Configuring the IdP within Cognito and mapping attributes (e.g., email, username) is crucial for successful authentication and authorization. This step establishes the trust relationship and allows Cognito to understand the user information coming from the SAML provider.
C: Configure the SAML identity provider to add the Amazon Cognito user pool as a relying party.
- Reasoning: This configures the trust relationship from the SAML IdP's perspective. By adding the Cognito User Pool as a relying party (or service provider), you're telling the SAML IdP that it's allowed to send assertions (authentication confirmations) to the Cognito User Pool. This is a standard SAML configuration step.
F: Update API Gateway to use a COGNITO_USER_POOLS authorizer.
- Reasoning: API Gateway's COGNITO_USER_POOLS authorizer allows you to protect your APIs by verifying the JWT (JSON Web Token) issued by the Cognito User Pool. When a user authenticates through the SAML-federated Cognito User Pool, they receive a JWT. API Gateway uses this JWT to authenticate and authorize the user before allowing access to the backend services (DynamoDB, in this case).

Incorrect Options:

A: Create a custom authorization service using AWS Lambda.
- Reasoning: While a custom Lambda authorizer is possible, it's an unnecessary complexity in this scenario. Cognito User Pools provide built-in SAML federation and JWT issuance, making the COGNITO_USER_POOLS authorizer a much simpler and more appropriate solution. Using Lambda would involve writing custom code to validate SAML assertions and manage authorization, which is already handled by Cognito.
D: Configure an Amazon Cognito identity pool to integrate with social login providers.
- Reasoning: Cognito Identity Pools (Federated Identities) are used to grant users access to AWS resources directly. They are designed for scenarios where users need to access AWS services like S3 or DynamoDB *from the client-side*. In this case, the application logic resides behind API Gateway, so you would use User Pools to authenticate the user and then authorize access to the backend via API Gateway. Also, the question specifies a SAML IdP, not social login providers.
E: Update DynamoDB to store the user email addresses and passwords.
- Reasoning: Storing user credentials directly in DynamoDB is a security risk and is generally bad practice, especially when a managed service like Cognito is available to handle authentication. Cognito is designed to securely manage user identities, including password storage (if you weren't using SAML). Furthermore, the question states the users already exist in a directory exposed through a SAML IdP. There is no need to migrate or duplicate those identities.

Citations:

Using SAML Federated Identity Providers With Amazon Cognito User Pools, https://docs.aws.amazon.com/cognito/latest/developerguide/cognito-user-pools-saml-identity-provider.html
কন্ট্রোলিং অ্যাক্সেস টু রেস্ট এপিআইস ইউজিং অ্যামাজন কগনিটো অরাইজারস, https://aws.amazon.com/blogs/compute/controling-access-to-rest-apis-using-amazon-cognito-authorizers/