The sum of all possible numbers that can be formed by using the digits $2, 3, 5, 7$ without repetition of digits is

The number of $9$-digit even natural numbers formed using only the digits $0$ and $1$,such that no two consecutive digits are $0$,is:

If ${}^n P_r = 30240$ and ${}^n C_r = 252$,then the ordered pair $(n, r)$ is equal to

The value of ${2^n} \{ 1 \cdot 3 \cdot 5 \cdots (2n - 3) \cdot (2n - 1) \}$ is

In an admission test,there are $15$ multiple-choice questions. Each question has $4$ alternatives. For each question,one or more than one answer can be correct. If a student attempts all $15$ questions and marks the answers randomly,in how many different ways can the student answer the question paper?

$n$ objects are distributed at random among $n$ persons. The number of ways in which this can be done so that at least one of them will not get any object is