Find the probability that in a random arrangement of the letters of the word $DAUGHTER$,the letter $D$ occupies the first place.

$A$ bag contains $3$ red,$7$ white,and $4$ black balls. If three balls are drawn from the bag,the probability that all of them are of the same color is:

There are $n$ different objects $1, 2, 3, \dots, n$ distributed at random in $n$ places marked $1, 2, 3, \dots, n$. The probability that at least three of the objects occupy places corresponding to their number is

An $URN$ contains $6$ blue,$4$ red,$3$ green and $2$ yellow marbles. If two marbles are picked at random,what is the probability that both are blue?

The probability that a man will be alive $25$ years hence is $0.3$ and the probability that his wife will be alive $25$ years hence is $0.4$. Find the probability that $25$ years hence,only the man will be alive.

$A$ problem in Mathematics is given to three students $A, B$,and $C$. Their respective probabilities of solving the problem are $\frac{1}{2}, \frac{1}{3}$,and $\frac{1}{4}$. What is the probability that the problem is solved?