CREATE TABLE table_4271 ("Route Number" FLOAT, "Origin" TEXT, "Intermediate stops" TEXT, "Destination" TEXT, "Provider" TEXT)

How many route numbers occur for the origin of Birmingham and destination of Bristol?
SELECT COUNT("Route Number") FROM table_4271 WHERE "Origin" = 'Birmingham' AND "Destination" = 'Bristol'
SELECT COUNT("Route Number") FROM "table_4271" WHERE "Destination" = 'Bristol' AND "Origin" = 'Birmingham'