OpenGL - Two different Element Array Buffers

Question

Can I have two different element array buffers? If yes, how to I bind them? Why is this wrong? It looks like only the second glDrawElements() works.

        glBindBuffer(GL_ARRAY_BUFFER, ebo1);
        glBindBuffer(GL_ELEMENT_ARRAY_BUFFER, ebo1);
        glDrawElements(GL_POLYGON, 6, GL_UNSIGNED_INT, 0);

        glBindBuffer(GL_ARRAY_BUFFER, ebo2);
        glBindBuffer(GL_ELEMENT_ARRAY_BUFFER, ebo2);
        glDrawElements(GL_POLYGON, 8, GL_UNSIGNED_INT, 0);