CREATE TABLE table_71110 ("Year" FLOAT, "Winner" TEXT, "Country" TEXT, "Score" FLOAT, "To par" TEXT, "1st prize  (  $  ) " FLOAT)

What is the total number of 1st prize ($) that has a United States country with a score lower than 271 and in a year after 1964 with a winner of Bobby Mitchell?
SELECT COUNT("1st prize ( $ )") FROM table_71110 WHERE "Country" = 'united states' AND "Score" < '271' AND "Year" > '1964' AND "Winner" = 'bobby mitchell'
SELECT COUNT("1st prize ( $ )") FROM "table_71110" WHERE "Country" = 'united states' AND "Score" < '271' AND "Winner" = 'bobby mitchell' AND "Year" > '1964'