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A dance team with 5 members will perform, 2 dancers at a

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A dance team with 5 members will perform, 2 dancers at a

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Source: Princeton Review

A dance team with 5 members will perform, 2 dancers at a time, until all the possible combinations of dancers have performed. If each combination dances for 5 minutes, and there are no breaks or interruptions, what is the total running time of the performance?

A. 80 minutes
B. 75 minutes
C. 60 minutes
D. 50 minutes
E. 45 minutes

The OA is D

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Total combinations 5c2 = 10
and each set performs for 5 minutes
So, total time ; 10*5 = 50.

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BTGmoderatorLU wrote:
Source: Princeton Review

A dance team with 5 members will perform, 2 dancers at a time, until all the possible combinations of dancers have performed. If each combination dances for 5 minutes, and there are no breaks or interruptions, what is the total running time of the performance?

A. 80 minutes
B. 75 minutes
C. 60 minutes
D. 50 minutes
E. 45 minutes

The OA is D
The number of combinations of dancers is 5C2 = (5 x 4)/2! = 10 and therefore the total running time of the performance is 10 x 5 = 50 minutes.

Answer: D

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5 members with 2 dancers at a time;
$$Possible\ combination=5_{C_2}=\frac{5\cdot4}{2\cdot1}=\frac{20}{2}=10 ways$$
$$The\ the\ total\ runtime\ of\ 5\ \min utes\ per\ 10\ ways\ =\ 5\cdot10=50\ \min utes\ \ \ \ \ \left(option\ D\right)$$

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