    Question

# Three numbers are chosen at random without replacement from {1,2,3,⋯,10}. The probability that, the smallest of the chosen number is 3 or the greatest one is 7, is equal to

A
740
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B
1140
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C
940
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D
1340
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Solution

## The correct option is B 1140Let E1 be the event: getting the smallest number 3 and E2 be the event: getting the greatest number 7 Then, P(E1)=P (getting one number 3 and other two from 4 to 10) =1C1×7C210C3=740 Similarly, P(E2)=P(getting one number 7 and other two number from 1 to 6) =1C1×6C210C3=18 P(E1∩E2)=P(getting one number 3 and second number 7 and third number from 4 to 6) =1C1×1C1×3C110C3=140 ∴P(E1∪E2)=P(E1)+P(E2)−P(E1∩E2) =740+18−140=7+5−140=1140  Suggest Corrections  0      Similar questions  Explore more