The number of ways in which first,second and third prizes can be given to $5$ competitors is

How many words can be formed using any $3$ letters from the word $UNIVERSAL$?

The number of arrangements that can be formed from the letters $a, b, c, d, e, f$ taken $3$ at a time without repetition,such that each arrangement contains at least one vowel,is

In how many ways can one send $6$ new-year greeting cards to $4$ people?

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 $4$-letter codes can be formed using the first $10$ letters of the English alphabet,if no letter can be repeated?