Let $n$ be a number of digits. Using the three digits $2, 5, 7$,at least $900$ distinct $n$-digit numbers can be formed. What is the minimum value of $n$?

The number of ways in which $6$ boys and $4$ girls can be arranged in a row such that between any two girls there must be exactly $2$ boys is

The number of ways in which $5$ boys and $3$ girls can be seated in a row so that each girl is between two boys.

In how many ways can one send $6$ new-year greeting cards to $4$ people?

For $n = 1, 2, 3, . . . , 50$,let $A = \{ a_n \mid a_n = \begin{cases} (-1)^{\frac{n}{2}} (\frac{n}{2}), & \text{if } n \text{ is even} \\ (-1)^{\frac{n-1}{2}} (\frac{n-1}{2}), & \text{if } n \text{ is odd} \end{cases} \}$ and $B$ be the set of all distinct elements of $A$. The number of permutations of all the elements of set $B$ such that even integers are in increasing order is:

Evaluate $7!$