A box contains 5 red balls and 3 blue balls. If two balls are drawn randomly without replacement, what is the probability that one of the balls is red and the other is blue?
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Use combinations to calculate probabilities when dealing with random draws without replacement.
The total count of balls is: \[ 5 + 3 = 8 \text{ balls}. \] The combinations for selecting 2 balls from 8 are: \[ \binom{8}{2} = \frac{8 \times 7}{2} = 28. \] The count of desired outcomes (one red ball and one blue ball) is: \[ \binom{5}{1} \times \binom{3}{1} = 5 \times 3 = 15. \] Consequently, the likelihood of selecting one red ball and one blue ball is: \[ \frac{15}{28}. \] The definitive answer is: \[ \boxed{\frac{15}{28}}. \]