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Problem Solving - Combinations

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Problem Solving - Combinations

by kavn » Wed Oct 19, 2011 5:39 am
A teacher is assigning 6 students to one of three tasks. She will assign students in teams of at least one student and all students will be assigned to teams. If each task will have eactly one team assigned to it, then which of the following are possible combinations of teams to tasks?

I 90
II 60
III 45

a - I only
b - I and II only
c - I and III only
d - II and III only
e - I,II,and III
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by user123321 » Wed Oct 19, 2011 1:00 pm
kavn wrote:A teacher is assigning 6 students to one of three tasks. She will assign students in teams of at least one student and all students will be assigned to teams. If each task will have eactly one team assigned to it, then which of the following are possible combinations of teams to tasks?

I 90
II 60
III 45

a - I only
b - I and II only
c - I and III only
d - II and III only
e - I,II,and III
since we need to take atleast 1 member in each team to form three teams and we have 6 members in our disposal, the possibilities are
2,2,2 or 1,2,3 or 1,1,4
if 2,2,2 team then 6!/2!*2!*2! = 90
if 1,2,3 team then 6c1*5c2 = 6*10 = 60
if 1,1,4 team then 6c1*5c1 = 6*5 = 30

so should be B

user123321
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