$A$ question paper contains $4$ questions,each having $4$ alternative answers. The number of ways that a candidate can answer one or more questions is

The value of ${}^6P_4 + 4 \cdot {}^6P_3$ is $.......$ .

The number of four-digit natural numbers which contain exactly two distinct digits is:

In a relay race there are five teams $A, B, C, D$ and $E$. What is the probability that $A, B$ and $C$ are the first three to finish (in any order)? (Assume that all finishing orders are equally likely.)

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

There are three sections in a question paper,each section containing $4$ questions. If a candidate has to answer exactly $5$ questions from this paper such that at least one question is answered from each section,then the number of ways in which a candidate can make the choice of questions is