Question

. Teams must each pick two different colors for their uniforms, from among 12 recognized colors. The 8 teams in the league each pick two colors, without consulting the other teams (and without regard to aesthetics!). If they choose at random, what is the probability that no two teams will have chosen the same pair of color

Answer 1

Answer:

The value is $P(X = 8) = 0.64$

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

$N = ^{12} C_2$

Here C stands for combination

=> $N = 66$

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

$P(8) = \ ^{N} P_8$

$P(8) = \ ^{66} P_8$

Here P stands for permutation

$P(8) =231580827878400$

Generally the total number of way the teams can select a pair of color is mathematically represented as

$P = (N)^8$

=> $P = (66)^8$

=> $P = 3.6004061*10^{14}$

Generally the the probability that no two teams will have chosen the same pair of color is mathematically represented as

$P(X = 8) = \frac{231580827878400}{3.6004061*10^{14}}$

=> $P(X = 8) = 0.64$