Answer:
The value is [tex]P(X = 8) = 0.64 [/tex]
Step-by-step explanation:
From the question we are told that
The number of recognized colors is n = 12
The number of teams is k = 8
Generally the total number of color pairs available to be selected is mathematically represented as
[tex]N = ^{12} C_2[/tex]
Here C stands for combination
=> [tex]N = 66 [/tex]
Generally the number of ways of selecting color pairs so that no two teams will have chosen the same pair of color is mathematically represented as
[tex]P(8) = \ ^{N} P_8[/tex]
[tex]P(8) = \ ^{66} P_8[/tex]
Here P stands for permutation
[tex]P(8) =231580827878400 [/tex]
Generally the total number of way the teams can select a pair of color is mathematically represented as
[tex]P = (N)^8[/tex]
=> [tex]P = (66)^8[/tex]
=> [tex]P = 3.6004061*10^{14}[/tex]
Generally the the probability that no two teams will have chosen the same pair of color is mathematically represented as
[tex]P(X = 8) = \frac{231580827878400}{3.6004061*10^{14}}[/tex]
=> [tex]P(X = 8) = 0.64 [/tex]
