If a five-digit number divisible by $3$ is to be formed using the digits $0, 1, 2, 3, 4,$ and $5$ without repetition,then the total number of ways this can be done is:

Consider all possible permutations of the letters of the word $ENDEANOEL$. Match the Statements / Expressions in $Column I$ with the Statements / Expressions in $Column II$.

$Column I$	$Column II$
$(A)$ The number of permutations containing the word $ENDEA$ is	$(p)$ $5!$
$(B)$ The number of permutations in which the letter $E$ occurs in the first and the last positions is	$(q)$ $2 \times 5!$
$(C)$ The number of permutations in which none of the letters $D, L, N$ occurs in the last five positions is	$(r)$ $7 \times 5!$
$(D)$ The number of permutations in which the letters $A, E, O$ occur only in odd positions is	$(s)$ $21 \times 5!$

Five-digit numbers are formed using the digits $1, 2, 3, 5, 7$ with repetitions and are written in descending order with serial numbers. For example,the number $77777$ has serial number $1$. Then the serial number of $35337$ is $.........$.

In how many ways can $5$ distinct balls be distributed among $3$ persons such that each person receives at least one ball?

How many six-digit numbers are there in which no digit is repeated,even digits appear at even places,odd digits appear at odd places,and the number is divisible by $4$?

The number of ways in which $4$ different things can be distributed to $6$ persons so that no person gets all the things is