The number of straight lines that can be formed by joining $8$ points on a circle is:

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

$^nC_r \div ^nC_{r-1} = $

Let $n$ be the number of different $5$-digit numbers,divisible by $4$,formed with the digits $1, 2, 3, 4, 5,$ and $6$,such that no digit is repeated in the numbers. What is the value of $n$?

$A$ person $X$ has four notes of $1, 2, 5,$ and $10$ denominations. The number of different sums of money she can form from them is

In how many different ways can the letters of the word '$AUCTION$' be arranged in such a way that the vowels always come together?