How many different five-letter passwords can be formed from the letters A, B, C, D, E, F, G and H if no repetition of letters is allowed? . .. five-letter words can be formed.

Alice and Bill have four grandchild, and they have three framed pictures of each grandchild. They wish to choose one picture of each grandchild to display on the piano in their living room, arranged from oldest to youngest. In how many ways can they do this?

How many ways can a committee of 3 freshmen and 4 juniors be formed from a group of 8 freshmen and 11 juniors?

In how many ways can 10 teenagers be seated at a round table if 2 girls wish to sit with their boyfriends.

Alice and Bill have four grandchildren, and they have three framed pictures of each grandchild. They wish to choose one picture of each grandchild to display on the piano in their living room, arranged from oldest to youngest. In how many ways can they do this?

A family consisting of 2 parents and 3 children is to pose for a picture with 2 family members in the front and 3 in the back a. How many arrangements are possible with no restrictions? b. How many arrangements are possible if the parents must sit in the front? C. How many arrangements are possible if the parents must be next to each other?

There are 10 applicants for three sales positions at a department store. All of the applicants are qualified. In how many ways can the department store fill the three positions?

At Rosemont High School, 14 players are on the varsity basketball team, 35 players are on the varsity football team, and 7 of these players are on both teams. How many different individual players are on the two varsity teams?

An Internet service provider requires its customer to select a password consisting of four letters followed by three digits. Find how many such passwords are possible in each of the following cases: a Repetition of letters and digits is allowed. b Repetition of letters and digits is not allowed.