1. A contractor needs 4 carpenters; ten are sent from the Union Hall. In how many ways can she pick her work crew? (1)

1. Miriam is going to her friend's wedding. She can select from 7 different dresses, 2 different hats, and 5 different purses. In how many ways can she select an outfit for the wedding that must include a dress, and a hat, and a purse? [1 mark]

1. The 7 members of the Prom Committee sit around a circular table. How many different seating arrangements are there of this group of people? [1 mark]

1. Rocco wants to make some pasta dishes. He needs 6 boxes of Spaghetti and 7 jars of Pasta Sauce. The shop had 11 boxes of Spaghetti and 12 jars of Pasta Sauce. How many ways could he make his selection? (3)

1. How many 3-digit numbers can be made from the digits 1 to 7 if no repetition is allowed and the number must be greater than 600? The first digit is either 6 or 7.
2. If it is 6 the last digit is either 3, 5, 7. The middle digit could be any of the remaining 4 not used. That's 3*4 = 12 possibilities.
3. If the first digit is 7, the last digit is either 3, or 5. The middle digit could be any of the remaining 4 not used. That's 2*4 =8.
4. So there are 12 + 8 = 20 possibilities.
5. [1 mark]

1. In how many ways can the letters of the word SPRAYING be arranged if A must be directly in front of Y ? [1 mark]
2. A committee of 6 is to be chosen from the 25 members of the student council which consists of 14 junior member and 11 senior members. In how many ways can this be done if the committee must include 4 juniors and 2 seniors? (3 marks)

1. Find the number of possible Canadian postal codes that end with a 3. Canadian postal codes have the form LDL DLD (where L is any letter in our alphabet and D is a digit from 0 to 9). For example, MGCI's postal code is M3C 1B3. [3 marks]

1. A committee of 5 people is to be chosen from a group of 10 volunteers consisting of 7 students and 3 teachers. In how many ways can this committee be formed if at least 2 teachers must be on the committee? [5 marks]

1. In how many ways can 12 players be seated on the team bench so that Fawad and Greg are NOT seated next to each other? Show all your work for full marks. [3 marks]

1. There are 16 teams entered in the Theatre Games tournament. In how many ways can first-place, second-place, and third-place ribbons be awarded to the teams? (1 mark)

1. In how many ways can a team of at least 4 people be formed from 6 people? [4 marks]

1. Sarah has 9 crayons: 3 blue, 1 red, 2 green, and 3 yellow. In how many ways can she line up the crayons on her desk? (2 marks)

1. There are 5 different colours available in a fabric that is suitable for a flag. How many different flags of 3 stripes, all vertical or all horizontal, (tricolours) can be made, assuming that NO colour is repeated in a flag? (2 marks)

1. How many 3-digit numbers are there if the number must be even? Repetition is allowed. [1]

1. We want to hang up photos of each family member in a row on the wall: Mum, Dad, Anni, Barb, Carlo & Dave. In how many ways could these 6 photos be hung in a row on the wall if the photos of Mum and Dad must be side by side (together; beside each other)? [2 marks]

1. Sam is handing out snacks at the day-care centre. There are 15 children. He has 7 apples, 6 oranges, and 2 bananas. In how many different ways could the snacks be distributed? (2)

1. I have 5 different letters. How many arrangements could be made using at least 3 letters for each arrangement? Show all your work for full marks. [4 marks]

1. There are 26 students in Anisa's class and we must have a team of 4 students for our contest.
2. In how many different ways could the team be chosen from the class? [1]

In how many different ways could the team be chosen if Anisa must be on the team? [1]