$A$ bag contains $3$ red,$4$ white,and $5$ black balls. Three balls are drawn at random. The probability that they are of different colours is

Let $m, n$ be two distinct integers chosen randomly from the set $\{0, 1, 2, \ldots, 99\}$. Then,the probability that $4^m + 4^n + 3$ is divisible by $5$ lies in the interval

Two persons $A$ and $B$ throw a pair of dice alternately until one of them gets the sum of the numbers appeared on the dice as $4$,and the person who gets this result first is declared as the winner. If $A$ starts the game,then the probability that $B$ wins the game is:

$A$ bag contains $6$ blue and $6$ green balls. Pairs of balls are drawn without replacement until the bag is empty. The probability that each drawn pair consists of one blue and one green ball is:

Out of a group of $10$ people,there are $5$ lawyers,$3$ doctors,and $2$ engineers. If $4$ people are selected at random,what is the probability that at least one person from each profession is included?

Four cards are drawn at random from a pack of $52$ playing cards. What is the probability that one card is drawn from each suit?