A set S is given by {1,2,3,4,5,6}. |X| is number of elements in set X. If A and B are independent eventsassociated with S are chosen such that each elements is equally likely and `1 le |B| le |A|` then the number of ordered pairs of (A,B) are

Answer

1523

Explanation

Number of ordered pair (A,B)
`.^(6)C_(1)(.^(6)C_(2)+.^(6)C_(3)+. . . .+.^(6)C_(6))+.^(6)C_(2)(.^(6)C_(3)+.^(6)C_(4)+.^(6)C_(5)+.^(6)C_(6))+.^(6)C_(3)(.^(6)C_(4)+.^(6)C_(5)+.^(6)C_(6))(.^(6)C_(5)+.^(6)C_(6))+.^(6)C_(5).^(6)C_(6)`
`=(.^(6)C_(1).^(6)C_(2)+.^(6)C_(3)+. . . .+.^(6)C_(5).^(6)C_(6))+(.^(6)C_(1).^(6)C_(3)+.^(6)C_(2).^(6)C_(4)+.^(6)C_(3).^(6)C_(5)+.^(6)C_(4).^(6)C_(6)`
`+(.^(6)C_(1).^(6)C_(4).^(6)C_(2).^(6)C_(5)+.^(6)C_(5).^(6)C_(6)+(.^(6)C_(1).^(6)C_(5)+.^(6)C_(2).^(6)C_(6))+(.^(6)C_(1).^(6)C_(6))`
`=(.^(12)C_(5)-.^(6)C_(1))+(.^(12)C_(4)-.^(6)C_(2))+(.^(12)C_(3)-^(6)C_(3))+(.^(12)C_(2)-.^(6)C_(4))+(.^(12)C_(1)-.^(6)C_(1))`
`=(.^(12)C_(1)+. . . .+.^(12)C_(5))-(.^(6)C_(1)+. . . .+.^(6)C_(4)+.^(6)C_(5))=1585-62=1523`