1. An event organizer is planing a program for a group of 20 people who want to embark on a sightseeing trip. Due to space constraints at the facilities to be visited the organizer partitions the group into five non-empty subgroups. The number of people in the subgroups may vary from one subgroup to another. (a) How many different partitions are there for the organizer? (b) How many different partitions are there if the second subgroup is made up of 4 people? (c) How many different partitions are there if the fourth subgroup is made up of 6 people?
1. An
(a) How many different partitions are there for the organizer?
(b) How many different partitions are there if the second subgroup is made up of 4 people?
(c) How many different partitions are there if the fourth subgroup is made up of 6 people?
(d) How many different partitions are there if the second and fourth subgroups have 4 and 6 people respectively?
(e) The organizer chooses a partition of the people at random. Find the probability that the number of people in the second and fourth subgroups of the chosen partition are not 4 and 6 respectively.
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