Two numbers are chosen from {1, 2, 3, 4, 5, 6, 7, 8} one after another without replacement. Then the probability thatA. the smallest value of two is less than 3 is `13//28`B. the bigger value of two is more than 5 is `9//14`C. product of two number is even is `11//14`D. none of these

Two numbers are chosen from {1, 2, 3, 4, 5, 6, 7, 8} one after another

1.	Two numbers are chosen from {1, 2, 3, 4, 5, 6, 7, 8} one after another without replacement. Then the probability thatA. the smallest value of two is less than 3 is `13//28`B. the bigger value of two is more than 5 is `9//14`C. product of two number is even is `11//14`D. none of these
Answer» Correct Answer - A::B::C Here total number of cases is `.^(8)C_(2) = 28` 1. Number of favorable case is 13. For 2 `rarr` 6 choices For 1 `rarr` 7 choices 2. For 6 `rarr` 5 choices For 7 `rarr` 6 choices For 8 `rarr` 7 choices 3. For 1 `rarr` 4 choices (2, 4, 6, 8) For 2 `rarr` 6 choices (3, 4, 5, 6, 7, 8) For 3 `rarr` 3 choices (4, 6, 8) For 4 `rarr` 4 choices (5, 6, 7, 8) For 5 `rarr` 2 choices (6, 8) For 6 `rarr` 2 choices (7, 8) For 7 `rarr` 1 choice (8) Alternate solution: a. `(.^(8)C_(2) - .^(6)C_(2))/(.^(8)C_(2)) = (13)/(28)` b. `(.^(8)C_(2)-.^(5)C_(2))/(.^(8)C_(2)) = (9)/(14)` c. `(.^(8)C_(2) - .^(4)C_(2))/(.^(8)C_(2)) = (11)/(14)`

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Two numbers are chosen from {1, 2, 3, 4, 5, 6, 7, 8} one after another without replacement. Then the probability thatA. the smallest value of two is less than 3 is `13//28`B. the bigger value of two is more than 5 is `9//14`C. product of two number is even is `11//14`D. none of these

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