Q. How many $4$-letter code can be formed using the first $10$ letters of the English alphabet, if no letter can be repeated?

Q. How many $3$-digit even numbers can be formed from the digits $1,2,3,4,5,6$ if the digits can be repeated?

Q. Given $5$ flags of different colours, how many different signals can be generated if each signal requires the use of $2$ flags, one below the other?

Q. How many $5$ digit telephone numbers can be constructed using the digits $0$ to $9$ if each number starts with $67$ and no digit appears more than once?

Q. A coin is tossed $3$ times and the outcomes are recorded. How many possible outcomes are there?

Q. How many $3$-digit numbers can be formed from the digits $1,2,3,4$ and $5$ assuming that.

Q. How many $3$-digit numbers can be formed from the digits $1,2,3,4$ and $5$ assuming that repetition of the digits is not allowed?

Q. Evaluate $\frac{n!}{(n-r)!}$, when
(i) $n=6,r=2$.

Q. Compute $\frac{8!}{6!\times 2!}$

Q. Evaluate $\frac{n!}{(n-r)!}$, when.
$n=9,r=5$.

Q. Evaluate
(i) $8!$ ii) $4!-3!$

Q. If $\frac{1}{6!}+\frac{1}{7!}=\frac{x}{8!}$, find $x$.

Q. Is $3!+4!=7!$ ?

Q. Evaluate-
(i) $4!-3!$

Q. Find n if ${}^{n-1}{P}_3{:}^n{P}_4=1:9$.

Q. How many $3$-digit even numbers can be made using the digits $1,2,3,4,6,7$ if no digit is repeated?

Q. Find the number of $4$-digit even numbers that can be formed using the digits $1,2,3,4,5$ if no digit is repeated. How many of those will be even?

Q. How many $4$-digit numbers are there with no digit repeated?

Q. How many $3$-digit numbers can be formed by using the digits $1$ to $9$ if no digit is repeated?

Q. From a committee of $8$ persons, in how many ways can we choose a chairman and a vice chairman assuming one person can not hold more than one position?