Paragraph: Let X= 1,2,3, ., 10 . A, B, C are three sets such that A X, B X and C X . Column-1: Contains types of three subsets of X . Column-2: Contains number of ways of selecting three subsets of X according to column-1 Column-3: Contains conditional probabilities P ( E E₁ ) or P ( E E₂ ) where E : Selecting three subsets of X according to column-1 E₁ : Selecting three subsets of X such that n(A B)=5E₂ : Selecting

Step-by-step solution

(I) A B C= 2,3,4,5,6 Each element of 1, 7, 8, 9, 10 has only two choices Number of ways =2^5 . (II) A B C= 3,4,5 Each element of 3, 4, 5 has 7 choices Number of ways =7^3=343 (III) A B C= 3,4,5,6,7 and A=B C Each element of 1,2, 8, 9, 10 has 3 choices Number of ways =3^5 but A=B C 3^5-1=242 (IV) A B C= 6,7,8,9,10 and A=B C Each element of 6, 7, 8, 9, 10 has 3 choices Number of ways =3^5 but A=B C 3^5-1=242 aligned & P ( E E₁ )= [ (I) ] According to 1 ¹⁰ C₅ 3^5 2¹⁰ = 1 ¹⁰ C₅ 12^5 & P ( E E₂ )= [ (I) ] According to 1