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?

Assuming that no two consecutive digits are same,the number of $n$-digit numbers is:

If $a$ denotes the number of permutations of $x + 2$ things taken all at a time,$b$ the number of permutations of $x$ things taken $11$ at a time,and $c$ the number of permutations of $x - 11$ things taken all at a time such that $a = 182bc$,then the value of $x$ is

All the letters of the word $ABRACADABRA$ are arranged in different possible ways. The number of such arrangements in which the vowels are together is:

How many $6$-digit numbers can be formed from the digits $0, 1, 3, 5, 7,$ and $9$ which are divisible by $10$,given that no digit is repeated?

How many $5$-digit numbers can be formed without any conditions?