A ball has three properties A,B,C with each property having three possible values: 1-”weak”, 2-”medium” ,...

A ball has three properties A,B,C with each property having three possible values: 1-”weak”, 2-”medium” , 3”strong” . For Example: A1,B3,C3 means that we have weak A, strong B and strong C ball. Consider the set of distinct balls. How many three ball subsets are there such that these 3 conditions hold (explain your answer):

Condition 1: All balls in the subset have the same value of A or all have diﬀerent values of A

Condition 2: All balls in the subset have the same value of B or all have diﬀerent values of B

Condition 3: All balls in the subset have the same value of C or all have diﬀerent values of C

Expert Solution

Number of distinct balls = 3*3*3 = 27

To satisfy all the conditions, the possible sets for A are ->

all three A1, all three A2, all three A3, (one A1, one A2 and one A3 in a total of 3! = 6 ways) , so the property A for a subset of 3 balls can have 9 different permutations

Similarly there can be 9 permutations for B and C as well

Thus, the number of three balls subsets with the following conditions = 9*9*9 = 729

orchestra answered 2 years ago

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