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Difficulty:
55%
(hard)
Question Stats:
64% (02:06) correct
36%
(01:54)
wrong
based on 301
sessions
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Six students in a social studies class will be divided into 3 pairs to give presentations about the continents Africa, Asia and South America. Each pair will be assigned a different continent. How many complete assignments of the 6 students to the 3 continents are possible ?
(A) 15
(B) 20
(C) 36
(D) 64
(E) 90
(A) 15
(B) 20
(C) 36
(D) 64
(E) 90
pierredmq
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Since there are 6 students, and we need presentations about 3 continents
(Asia, Africa and South America) and a pair of students each to give these presentations.
For Asia, there would be \(6c2(15)\) ways of choosing the students
For Africa, there would be \(4c2(6)\) ways of choosing the students
For South America, there would be \(2c2(1)\) way of choosing the students
Total ways possible of choosing the students is 15*6*1 = 90 ways(Option E)
(Asia, Africa and South America) and a pair of students each to give these presentations.
For Asia, there would be \(6c2(15)\) ways of choosing the students
For Africa, there would be \(4c2(6)\) ways of choosing the students
For South America, there would be \(2c2(1)\) way of choosing the students
Total ways possible of choosing the students is 15*6*1 = 90 ways(Option E)
General Discussion
Posts: 8
Number of different pairs of students: 6C2 = 15 pairs
Each pair can be assigned 3 countries = 45 different total assignments for pairs
Each pair has 2 students, so 2*45 = 90 total different assignments
Each pair can be assigned 3 countries = 45 different total assignments for pairs
Each pair has 2 students, so 2*45 = 90 total different assignments
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