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Q.

Two numbers are chosen from {1,2,3, 4, 5, 6,7,8} one after another without replacement. Then the probability that

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a

the smaller 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 is A.

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Detailed Solution

Here total number of cases is  8C2=28.1. Number of favorable case is 13.For 2 → 6 choicesFor 1 → 7 choices2. For 6 → 5 choicesFor 7 → 6 choicesFor 8 → 7 choices3. For 1 → 4 choices (2, 4, 6, 8)For 2 → 6 choices (3, 4, 5, 6,7, 8)For 3 → 3 choices (4, 6, 8)For 4 → 4 choices (5, 6, 7, 8)For 5 → 2 choices (6, 8)For 6 → 2 choices (7, 8)For 7 → 1 choice (8)Alternate solution:a.  8C2−6C2 8C2=1328b.  8C2−5C2 8C2=914c.  8C2−4C2 8C2=1114
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