How many $3$-digit numbers can be formed by using the digits $1$ to $9$ if no digit is repeated?

If all the digits in the number $53426$ are permuted in all possible ways and are arranged in decreasing order,then the number having rank $89$ is:

The number of all four-digit numbers that can be formed with the digits $0, 1, 2, 3, 4, 5$ when the repetition of the digits is not allowed,is

On the occasion of the Dipawali festival,each student of a class sends a greeting card to every other student. If there are $20$ students in the class,the total number of greeting cards sent by the students is:

Find the number of arrangements of the letters of the word $INDEPENDENCE$. In how many of these arrangements do the words start with $P$?

The number lock of a suitcase has $4$ wheels,each labelled with ten digits,i.e.,from $0$ to $9$. The lock opens with a sequence of four digits with no repeats. What is the probability of a person getting the right sequence to open the suitcase?