There were 16 students in my previous grad course, 6 from civil, 5 from TTP and

Question

There were 16 students in my previous grad course, 6 from civil, 5 from TTP and 5 from other schools. a) For a conference, I wanted to select a group of 5 students to take with me. How many ways could I arrange this group of students? b) From the class I also wanted to select a main presenter, a poster presenter and Q&A; individual. How many ways could I fill these three positions. c) As a backup, considering funding, I wanted to split the class in 3 subgroups arranged. One with 3 students, one with 6 and one with 7. How many ways can these subgroups be formed

Explanation / Answer

ANSWER:

Total number of students = 16

(a) number of ways of arranging a group of 5 students from 16 students = ^{16}P_5

(b) we need one main presenter that can be selected in 16C1 ways,

One poster presented that can be selected in 15C1 ways, (because after selecting one main presenter, only 15 people are left to choose from) and,

One Q&A individual that can be selected in 14C1 ways.

So the total number of ways of selecting these 3 people =^{16}C_1 imes ^{15}C_1 imes ^{14}C_1 ways

(C) we need 3 sub groups of 3,6 and 7 people.

This can be done in :

^{16}C_3 imes ^{13}C_6 imes ^{7}C_7 ways

Note : in the first case, the arrangement of the people matters, so we used permutation. While in the next two cases, the arrangement of the people does not matter, so we have used combination

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