In a box there are ten cards on which the numbers from 0 to 9 have been written successively. We take three cards out of the box using two methods and consider the probabilities. (1) We take out three cards simultaneously. (i) The probability that each number on the three cards is 2 or more and 6 or less is $\dfrac{\mathbf{KL}}{\mathbf{MN}}$. (ii) The probability that the smallest number is 2 or less and the greatest number is 8 or more is $\dfrac { \mathbf { N O } } { \mathbf { P Q } }$. (2) Three times we take out one card from the box, check its number, and then return it to the box. The probability that the smallest number is 2 or more and the greatest number is 6 or less is $\dfrac { \mathbf { R } } { \mathbf { S } }$.
In a box there are ten cards on which the numbers from 0 to 9 have been written successively. We take three cards out of the box using two methods and consider the probabilities.
(1) We take out three cards simultaneously.
(i) The probability that each number on the three cards is 2 or more and 6 or less is $\dfrac{\mathbf{KL}}{\mathbf{MN}}$.
(ii) The probability that the smallest number is 2 or less and the greatest number is 8 or more is $\dfrac { \mathbf { N O } } { \mathbf { P Q } }$.
(2) Three times we take out one card from the box, check its number, and then return it to the box. The probability that the smallest number is 2 or more and the greatest number is 6 or less is $\dfrac { \mathbf { R } } { \mathbf { S } }$.