If letters of the word $PENCIL$ are arranged in random order,what is the probability that $N$ is always next to $E$?

$A$ 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:

An unbiased die is tossed until a number greater than $4$ appears. The probability that an even number of tosses is needed is

If out of $20$ consecutive whole numbers two are chosen at random,then the probability that their sum is odd,is

There are $3$ urns $A, B$,and $C$. Urn $A$ contains $4$ red balls and $3$ black balls. Urn $B$ contains $5$ red balls and $4$ black balls. Urn $C$ contains $4$ red balls and $4$ black balls. One ball is drawn from each of these urns. What is the probability that the $3$ balls drawn consist of $2$ red balls and $1$ black ball?

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