If there is a box with seven white balls and five red balls. Two balls are drawn at random, what is the probability that one ball is white and the other red?

7 white and 5 red.

so choose 1 from seven white balls and 1 from 5 red balls.

this can be done in ⁷c₁ x ⁵c_{1 = 35}

total possibilities = ¹²c₂ = 66.

so probability = 35