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Let `|X|` dentoe the number of elements in a set `X`. Let `S={1,2,3,4,5,6}` be a sample space, where each element is equally likely to occur. If A and B are independent events associated with S, then the number of ordered paris , `(A,B)` such that `1le|B|lt|A|`, equals............ |
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Answer» Correct Answer - `1523` Given sample space S `={1,2,3,4,5,6}` andlet there are `i` elements in set A an j elements in set B, Now, according to information `1 le j lt I le 6`. So, total number of ways of choosing sets A and `B=sum_(1lejltile6)(sum" "sum) .^(6)C_(i)" ".^(6)C_(j)` `=((underset(r=1)overset(6)(sum).^(6)C_(r))^(2)-underset(r=1)overset(6)(sum)(.^(6)C_(r))^(2))/(2)=((2^(6)-1)^(2)-(.^(12)C_(6)-1))/(2)` `=((63)^(2)-(12!)/(6!6!)+1)/(2)` `=(3969-924+1)/(2)=(3046)/(2)=1523` |
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