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Three numbers are chosen at random witho...

Three numbers are chosen at random without replacement from {1, 2, 3, …, 10}. Find the probability that the smallest of the chosen numbers is 3, or the greatest one is 7.

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The correct Answer is:
A
Let `E_(1)` be the event getting minimum number 3 and `E_(2)` be the event getting maximum number 7.
Then, `P(E_(1))=P` (getting one number 3 and other two from numbers 4 to 10)
`(overset(1)""C_(1)xxoverset(7)""C_(2))/(overset(10)""C_(3))=(7)/(40)`
`P(E_(2))=P` (getting one number 3, second number 1 to 6)
`(overset(1)""C_(1)xxoverset(1)""C_(1)xxoverset(3)""C_(1))/(overset(10)""C_(3))=(1)/(10)`
`:. P(E_(1)uuE_(2))=P(E_(1))+P(E_(2))-P(E_(1)nnE_(2))`
`=(7)/(40)+(1)/(8)-(1)/(40)=(11)/(40)`
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