How many ways are there to distribute 6 different books among 13 children if no child gets more than 1 book?

In a certain state, license plates each consist of 3 letters from the English alphabet, followed by 3 digits. How many different license plates are there that have no repeated letters or digits?

Suppose you are interviewing 25 people in order to fill 5 job vacancies. How many possible choices of 5 people are there to fill those vacancies?

How many different ID cards can be made if you must choose 7 digits followed by 2 letters and any letter or number can repeated?

How many ways can a jury of four men and three women be selected from twelve men and ten women? Please show all your . Thank you.

How many ways can 6 people be chosen and arranged in a straight line if there are 8 people to chose from?

Among 10 student clubs recruiting new members this year, how many ways are there to choose 8 clubs out of 10 to join?

20 different comic books will be distributed to 5 kids. 1) How many ways are there to distribute the comic books if there are no restrictions on how many go to each kid (other than the fact that all 20 will be given out)? 2) How many ways are there to distribute the comic books if they are divided evenly so that 4 go to each kid??

How many ways are there to seat 6 different boys and 6 different girls along one side of a long table with 12 seats? How many ways are there IF boys and girls alternate seats?