The sum of the digits in the unit's place of all the $4-$digit numbers formed by using the digits $3, 4, 5,$ and $6$,without repetition,is

If $^nP_5 = 9 \times ^{n-1}P_4$,then the value of $n$ is

From among the $36$ teachers in a school,one principal and one vice-principal are to be appointed. In how many ways can this be done?

Consider all possible permutations of the letters of the word $EARTHQUAKE$. The number of permutations containing the word $RAHU$ is:

In how many different ways can the letters of the word '$CORPORATION$' be arranged so that the vowels always come together?

If the number of $5$-element subsets of the set $A = \{a_1, a_2, \dots, a_{20}\}$ of $20$ distinct elements is $k$ times the number of $5$-element subsets containing $a_4$,then $k$ is