Suppose that there are five students enrolled in a chemistry laboratory class. T
ID: 3204511 • Letter: S
Question
Suppose that there are five students enrolled in a chemistry laboratory class. They will have to complete five lab assignments. For each lab assignment, four of the students will work in two pairs while one student works independently. Each student will work independently for exactly one of the five labs. Each student will work with each of the other four students exactly once. How many different lab schedules are possible? First, suggest one possible schedule for the five labs. Then produce an answer to the question with an explanation of your reasoning.
Explanation / Answer
let’s assign the five students as A,B,C,D,E
The conditions given are
To find: no of schedules possible?
if A is working independently, then the combinations we have are
A
B,C
D,E
A
B,D
C,E
A
B,E
C,D
similarly, the combinations for other students are
B
B
A,C
D,E
B
A,D
C,E
B
A,E
C,D
C
C
A,B
D,E
C
A,D
B,E
C
A,E
B,D
D
D
A,B
C,E
D
A,C
B,E
D
A,E
B,C
E
E
A,B
C,D
E
A,C
B,D
E
A,D
B,C
now we need to suggest a schedule which meets all the criteria/conditions
lets consider line 1 of A working independently
A
B,C
D,E
then we have 2 combinations for B working independently
B
A,D
C,E
B
A,E
C,D
B
A,C
D,E
is not possible as event D,E has already occurred when A is working independent
Hence, we have a total of 2 combinations
A
B,C
D,E
A
B,C
D,E
B
A,D
C,E
B
A,E
C,D
C
C
D
D
E
E
working in the similar way, the final schedule will be
A
B,C
D,E
A
B,C
D,E
B
A,D
C,E
B
A,E
C,D
C
A,E
B,D
C
A,D
B,E
D
A,C
B,E
D
A,B
C,E
E
A,B
C,D
E
A,C
B,D
similarly, if we consider line 2 and line 3 for A working independent
we will figure out the below 4 combinations
A
B,D
C,E
A
B,D
C,E
B
A,C
D,E
B
A,E
C,D
C
A,D
B,E
C
A,B
D,E
D
A,E
B,C
D
A,C
B,E
E
A,B
C,D
E
A,D
B,C
A
B,E
C,D
A
B,E
C,D
B
A,C
D,E
B
A,D
C,E
C
A,E
B,D
C
A,B
D,E
D
A,B
C,E
D
A,E
B,C
E
A,D
B,C
E
A,C
B,D
hence, we have a total of 6 different lab schedules possible for the chemistry lab assignment
A
B,C
D,E
A
B,C
D,E
B
A,D
C,E
B
A,E
C,D
C
A,E
B,D
C
A,D
B,E
D
A,C
B,E
D
A,B
C,E
E
A,B
C,D
E
A,C
B,D
A
B,D
C,E
A
B,D
C,E
B
A,C
D,E
B
A,E
C,D
C
A,D
B,E
C
A,B
D,E
D
A,E
B,C
D
A,C
B,E
E
A,B
C,D
E
A,D
B,C
A
B,E
C,D
A
B,E
C,D
B
A,C
D,E
B
A,D
C,E
C
A,E
B,D
C
A,B
D,E
D
A,B
C,E
D
A,E
B,C
E
A,D
B,C
E
A,C
B,D
A
B,C
D,E
A
B,D
C,E
A
B,E
C,D
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.