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

How many $5$-digit numbers can be formed using the digits $3, 4, 7$ once each and the digit $5$ twice?

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 . . . . . . .

${ }^{15} P_8 = A + 8 \cdot { }^{14} P_7 \Rightarrow A = $

How many words can be formed using the letters of the word $BHARAT$ such that $B$ and $H$ never come together?

$n$ cadets have to stand in a row. If all possible permutations are equally likely,then the probability that two particular cadets stand side by side is