In a shoe rack,there are $4$ pairs of shoes. If $4$ shoes are drawn one after the other at random without replacement,what is the probability of getting at least one correct pair of shoes among the four shoes drawn?

$A$ bag contains $13$ red,$14$ green,and $15$ black balls. The probability of getting exactly $2$ black balls when pulling out $4$ balls is $P_1$. Now,the number of balls of each color is doubled,and $8$ balls are pulled out. The probability of getting exactly $4$ black balls is $P_2$. Then:

$A$ bag contains $3$ white and $6$ red balls. Four balls are drawn at a time randomly. The probability of getting at least $2$ red balls is:

If a $5$-digit number is chosen at random,what is the probability that all digits are distinct,odd digits occupy odd places,and even digits occupy even places?

$A$ bag contains $12$ pairs of socks. If $4$ socks are picked up at random,the probability that there is at least one pair is equal to

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