Yes, BX cable (also known as armored cable) can be installed in a plastic box. However, the size of the box must be appropriate for the number and size of wires being installed. The National Electrical Code (NEC) provides guidelines for calculating the minimum size requirements for the box based on the number and size of conductors. It’s important to follow these guidelines to ensure that the electrical installation is safe and meets code requirements. Additionally, make sure that the plastic box is rated for the application and is compatible with the type of cable being installed.