How many words of $7$ letters can be formed by selecting $4$ consonants and $3$ vowels from $6$ consonants and $5$ vowels?

Three persons enter a lift at the ground floor. The lift goes up to the $10^{\text{th}}$ floor. If the lift does not stop at the $1^{\text{st}}$, $2^{\text{nd}}$, and $3^{\text{rd}}$ floors, the number of ways in which the three persons can exit the lift at three different floors is equal to . . . . . . .

How many words can be formed using the letters of the word $MOBILE$ such that the consonants always occupy odd positions?

If all possible numbers are formed by using the digits $1, 2, 3, 5, 7$ without repetition and they are arranged in descending order,then the rank of the number $327$ is

The teacher wants to arrange $5$ students on the platform such that the boy $B_1$ occupies the second position and the girls $G_1$ and $G_2$ are always adjacent to each other. Then,the number of such arrangements is

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?