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Answer:
The total number of ways to form a student governance committee is 1,211,760.
Step-by-step explanation:
The students senate consists of a total of 40 students.
The students are either Sophomores or Juniors or Seniors.
The number of students in each of these categories are as follows:
Sophomores = 18
Juniors = 12
Seniors = 10
A governance committee have to be selected from the students senate.
The committee have to made up of 2 sophomores, 2 juniors and 3 seniors.
Combinations can be used to select 2 sophomores from 18, 2 juniors from 12 and 3 seniors from 10.
Combinations is a mathematical technique used to determine the number of ways to select <em>k</em> items from <em>n</em> distinct items.
The formula is:
(1)
Compute the number of ways to select 2 sophomores from 18 as follows:
Thus, there are 153 ways to select 2 sophomores from 18.
(2)
Compute the number of ways to select 2 juniors from 12 as follows:
Thus, there are 66 ways to select 2 juniors from 12.
(3)
Compute the number of ways to select 3 seniors from 10 as follows:
Thus, there are 120 ways to select 3 seniors from 10.
The total number of ways to form a student governance committee that must have 2 sophomores, 2 juniors and 3 seniors is:
Total number of ways =
Thus, the total number of ways to form a student governance committee is 1,211,760.