$A$ mapping is selected at random from the set of all the mappings of the set $A = \{1, 2, ..., n\}$ into itself. The probability that the mapping selected is an injection is

An urn contains $8$ red and $5$ white balls. Three balls are drawn at random. Then, the probability that balls of both colours are drawn is

If three distinct numbers are selected from the first $100$ natural numbers,what is the probability that all selected numbers are divisible by both $2$ and $3$?

Two persons $A$ and $B$ take turns in throwing a pair of dice. The first person to throw a sum of $9$ with both dice will be awarded the prize. If $A$ throws first,then the probability that $B$ wins the game is

$A$ box contains $8$ red and $7$ black balls. If two balls are drawn at random,the probability that both balls are of the same color is ...... .

$A$ box contains $2$ black,$4$ white and $3$ red balls. One ball is drawn at random from the box and kept aside. From the remaining balls in the box,another ball is drawn at random and kept aside the first. This process is repeated until all the balls are drawn from the box. The probability that the balls drawn are in the sequence of $2$ black,$4$ white and $3$ red is