In a club election,the number of contestants is one more than the maximum number of candidates for which a voter can vote. If the total number of ways in which a voter can vote is $62$,then the number of candidates is:

The number of times the digit $3$ will be written when listing the integers from $1$ to $1000$ is

In how many different ways can three persons $A, B, C$ having $6, 7$ and $8$ one-rupee coins respectively,donate $₹ 10$ collectively?

How many different words can be formed by jumbling the letters in the word $MISSISSIPPI$ in which no two $S$ are adjacent?

$A$ building has a ground floor and $10$ more floors. Nine persons enter a lift at the ground floor. The lift goes up to the $10$th floor. The number of ways in which any $4$ persons exit at a floor and the remaining $5$ persons exit at a different floor,if the lift does not stop at the first and the second floors,is equal to:

Let the digits $a, b, c$ be in $A.P.$ Nine-digit numbers are to be formed using each of these three digits thrice such that three consecutive digits are in $A.P.$ at least once. How many such numbers can be formed?