$A$ five-digit number is formed using the digits $1, 2, 3, 4, 5$ without repetition. What is the probability that the number is divisible by $4$?

If an unbiased dice is rolled thrice,then the probability of getting a greater number in the $i^{\text{th}}$ roll than the number obtained in the $(i-1)^{\text{th}}$ roll,for $i=2, 3$,is equal to: (in $/54$)

$A$ $5$-digit number is formed using the digits $1, 2, 3, 4, 5, 6,$ and $8$. What is the probability that the number has even digits at both ends?

Let $S$ be the set of all the words that can be formed by arranging all the letters of the word $\text{GARDEN}$. From the set $S$,one word is selected at random. The probability that the selected word will $\text{NOT}$ have vowels in alphabetical order is:

$A$ bag contains $6$ red,$5$ white and $4$ black balls. Two balls are drawn. The probability that none of them is red,is

If $m$ rupee coins and $n$ ten paise coins are placed in a line,then the probability that the extreme coins are ten paise coins is