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A total of 12 players consisting 6 male and 6 female badminton players are attending a training camp.
(a) During a morning activity of the camp, these 12 players have to randomly group into six pairs of two players each.
(i) Find the total number of possible ways that these six pairs can be formed.
(ii) Find the probability that each pair contains players of the same gender only. Correct your final answer to 4 decimal places.
(b) During an afternoon activity of the camp, 6 players are randomly selected and 6 one-on-one matches with the coach are to be scheduled.
(i) How many different schedules are possible?
(ii) Find the probability that the number of selected male players is higher than that of female players given that at most 4 females were selected. Correct your final answer to 4 decimal places.
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