$4$ cards are drawn from a well-shuffled deck of $52$ cards. What is the probability of obtaining $3$ diamonds and $1$ spade?

$A$ bag contains $3$ red,$4$ white,and $5$ black balls. If three balls are drawn at random,what is the probability that they are of different colors?

$A$ box contains $50$ tickets numbered $1, 2, 3, \dots, 50$. Five tickets are drawn at random and arranged in ascending order $(x_1 < x_2 < x_3 < x_4 < x_5)$. What is the probability that $x_3 = 30$?

Two different families $A$ and $B$ are blessed with an equal number of children. There are $3$ tickets to be distributed amongst the children of these families so that no child gets more than one ticket. If the probability that all the tickets go to the children of family $B$ is $\frac{1}{12}$,then the number of children in each family is?

There are $6$ positive and $8$ negative numbers. If four numbers are chosen at random and multiplied,the probability that the product is a negative number is

$A$ bag contains $6$ white and $4$ black balls. Two balls are drawn at random. The probability that they are of the same colour is . . . . . .