Given that a throw of three unbiased dice shows different faces,what is the probability that their total is eight?

$A$ box contains $6$ bottles of $V_1$ drink,$3$ bottles of $V_2$ drink and $4$ bottles of $V_3$ drink. If three bottles are drawn at random,then the probability that the three are not of the same variety is

If the coefficients $a$ and $b$ of a quadratic expression $x^2+ax+b$ are chosen from the sets $A=\{3, 4, 5\}$ and $B=\{1, 2, 3, 4\}$ respectively, then the probability that the equation $x^2+ax+b=0$ has real roots is

If $A_1, A_2, \ldots, A_{15}$ are the events of a random experiment, then which one of the following is true?

Two numbers are selected at random from the first $40$ natural numbers. What is the probability that their sum is odd?

If $3$ dice are thrown, the probability of getting $10$ as the sum of the three numbers that appeared on the top faces of the dice is