The number of positive integral solutions of $abc = 30$ is

An examination has $3$ multiple-choice questions,and each question has $4$ options. If a student passes only if they answer all questions correctly,in how many ways can they fail?

The number of integers between $1$ and $10^{10}$ (inclusive) that contain the digit $1$ is:

What is the remainder when $1! + 2! + 3! + \dots + 200!$ is divided by $14$?

$A$ group of students comprises $5$ boys and $n$ girls. If the number of ways,in which a team of $3$ students can be randomly selected from this group such that there is at least one boy and at least one girl in each team,is $1750$,then $n$ is equal to

Find the remainder when $(1!)^2 + (2!)^2 + (3!)^2 + \dots + (100!)^2$ is divided by $10^2$.