Answer:
P = 1 /362880
Where the numerator is the event of selecting the same order as last performance that is 1.
The denominator is the total number of possible events of selecting the 9 dancers.
p = 1/72
Therefore, there is a 1/72 probability that the team puts the top hip hop dancer in the third position and top break dancer in the first position.
Step-by-step explanation:
The probability that the team selects the same order as last performance is 1 divided by 362880
Explain where each the numerator and denominator come from
The probability that the team selects the same order as last performance is
P = 1 /362880
Where the numerator is the event of selecting the same order as last performance that is 1.
The denominator is the total number of possible events of selecting the 9 dancers.
Total number of dancers = 9
The 1st dancer can be selected in 9 ways
The 2nd dancer can be selected in 8 ways
The 3rd dancer can be selected in 7 ways
The 4th dancer can be selected in 6 ways
The 5th dancer can be selected in 5 ways
The 6th dancer can be selected in 4 ways
The 7th dancer can be selected in 3 ways
The 8th dancer can be selected in 2 ways
The 9th dancer can be selected in 1 ways
So the total number of ways = 9×8×7×6×5×4×3×2×1 = 362880
What is the probability that the team puts the top hip hop dancer in the third position and top break dancer in the first position?
Lets us put the top hip hop dancer in the third position and top break dancer in the first position then the remaining 7 dancers can be selected in
7×6×5×4×3×2×1 = 5040 ways
So the required probability is,
P = 5040/362880
P = 1/72
P = 0.0139
Therefore, there is a 1/72 probability that the team puts the top hip hop dancer in the third position and top break dancer in the first position.
