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Question

# Three numbers are chosen at random without replacement from 1,2,....10 . The probability that the minimum of the chosen numbers is 3, or their maximum is 7 is ..............

A
7/24
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B
11/40
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C
17/60
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D
1/4
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Solution

## The correct option is B 11/40Let A and B denote the following events:A:minimum of the chosen number is 3B: maximum of the chosen number is 7We have,P(A)=P(choosing 3 and two other numbers from 4 to 10)=7C210C3=7×62×3×210×9×8=740P(B)=P(choosing 7 and two other numbers from 1 to 6)=6C210C3=6×52×3×210×9×8=18P(A∩B)=P(Choosing 3 and 7 and one other number from 4 to 6)=310C3=3×3×210×9×8=140Now P(A∪B)=P(A)+P(B)−P(A∩B)=740+18−140=1140

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