$1.$ State Diagram

Design a state diagram for an online bookstore's order management system. This system should track the state of an order from the moment it is placed by the customer until it is delivered. The main states should include Order Placed, Processing, Shipped, In Transit, and Delivered. Also, include necessary transitions based on events like payment confirmation, dispatch, and delivery confirmation.

Key States and Transitions:

$1.$ States:

$-$Order Placed

$-$Processing

$-$Shipped

$-$In Transit

$-$Delivered

$-$Order Cancelled $($an additional state to handle cancellations$)$

$2.$ Transitions:

$-$Order Placed to Processing: Triggered by payment confirmation.

$-$Processing to Shipped: Triggered when the order is dispatched.

$-$Shipped to In Transit: Triggered when the carrier starts delivery.

$-$In Transit to Delivered: Triggered when the order is delivered to the customer.

$-$Any state to Order Cancelled: Triggered by order cancellation $($before delivery$).$

$3.$ Considerations for the Diagram:

$-$Initial State: Begins at 'Order Placed.$\text{'}$

$-$Final State: Ends at 'Delivered' or 'Order Cancelled.$\text{'}$

$-$Transition Arrows: Should clearly indicate the direction of the workflow.

$-$Events: Label transitions with events that cause the state change.