Five horses are in a race. $Mr. A$ selects two of the horses at random and bets on them. The probability that $Mr. A$ selected the winning horse is

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 $/54$)

Three numbers are chosen at random without replacement from the set $A = \{x \in \mathbb{Z} \mid 2 \leq x \leq 11\}$. The probability that the minimum of the chosen numbers is $3$ and the maximum is $7$ is

There are $n$ letters and $n$ addressed envelopes. The probability that each letter is placed in the correct envelope is

An urn contains $6$ yellow balls and $x$ black balls. When two balls are drawn at random,the probability that both are yellow is $\frac{5}{26}$,then the value of $x$ 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