Question 6 (8 marks) It is Lady Bridgerton's first ball of the season and she must select 3 dance partners for the upcoming dances. She cannot dance with the same partner twice. Of the 10 potential dance partners at the ball, there are 2 Dukes, 3 Earls, and 5 Barons. Find the probability that: a) she does not dance with an Earl. (2 marks) b) she dances with exactly 1 Duke. (2 marks) c) she dances with at least one Baron. (2 marks) d) each dance partner has a different rank. (2 marks)