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

Explanation

Let `E_(1)` be the event ''getting smallest number 3''. And `E_(2)` be the event ''getting greatest number 7'' Then, `P(E_(1))` = P(getting one number 3 and other two from number 4 to 10)
`=(.^(1)C_(1)xx.^(7)C_(2))/(.^(10)C_(3))= (7)/(40)`
Similarly,
`P(E_(2))`=P (getting one number 7 and other 2 from numbers 1 to 6)
`=(.^(1)C_(1)xx.^(6)C_(2))/(.^(10)C_(3))= (1)/(8)`
`P(E_(1) nn E_(2)) = P` (getting one number 3 second number 7 and third from number from 4 to 6)
`=(.^(1)C_(1)xx.^(1)C_(1)xx.^(3)C_(1))/(.^(10)C_(3))=(1)/(40)`
`therefore P(E_(1) uu E_(2)) = P(E_(1)) + P(E_(2)) - P(E_(1)nn E_(2))`
`=(7)/(40) + (1)/(8) - (1)/(40)`
`= (7 + 5 - 1)/(40) = (11)/(40)`