Permutations and Combinations

1. Karen owns 4 pairs of pants, 7 shirts, and 3 sweaters. In how many ways may she choose 2 of the pairs of pants, 3 of the shirts, and 1 of the sweaters to pack for a trip?

2. How many permutations are there of the letters in the name 'Jonathan"?

3. Five students in the GLA charity club are going to line up for a photo. 2 of the students do not want to stand next to each other in the picture. In how many ways may these students line up if the two will not stand next to each other?

4. The boys' soccer team plays 10 games during the school year. In how many ways can the team end the season with 5 wins, 4 losses, and 1 tie?

5. Lorey enjoys football. She has a pair of tickets to 6 different Seattle Seahawks home games. If Lorey has five football-loving friends, how many ways may she take one of them along to each of the six games?

6. In a schools student council election there are four candidates for President, five candidates for treasurer, and two candidates for secretary. In how many ways may the student voters mark their ballots

a) if they vote in all three of the races?

b) if they exercise their right not to vote in any or all of the races?

7. At the Ontario's science fair there are five finalists. In how many ways may the judges choose a winner and a first runner-up?

8. The biology exam is a multiple-choice test that consists of 15 questions. Each question has 5 options to choose from. In how many ways may a student fill in the answers if they answer each question?