Test – Intro to Probability (SHOW WORK FOR FULL MARKS)

Part A: Knowledge

For questions 1 – 4, circle the letter that corresponds to the best answer.   No steps required.        [         /4K]

  1. What is the same as 6!?
A. 6P6B. 6P1C. 6C6D. 6C1
  1. I have 10 identical flags. Four are red and 6 are blue. How many arrangements can I make?
A. 10!B. 10C1C. 10P6D.
  1. How many ways can we seat 4 people seat in a circle
A. 24B. 6C. 4D. 20
  1. I need to come up with a new 4-digit alarm code. If the numbers cannot repeat and can be any digit from 0-9 how many codes are there?
A. 104B. 4!
C. 10C4D. 10P4  

             6.   We have the following desserts to choose from: four Carrot cakes, five Chocolate cakes and two Vanilla cakes. How many ways can we select;

                    a) We have at least one dessert (1K)

                    b) If we want exactly one cake (1K)

                    c) If we want at least two Chocolate cakes (2K)

7.  A classroom of 8 people are lining up to take a picture. How many ways can they take a picture if:

a) There are no restrictions (1A)

b) They are standing in a circle (1A)

c) If Hiba, Navreen and Emelia must be together (1A)

d) If Afzal and Daniel are not together (2A)

e) If Leon is first and Hiba, Afzal and Daniel are together with Zain and Navreen together. (3A)

9.  Subway claims to have over 2 billion types of subs that you can make with their, 16 types of meats 15 types of vegetables and 8 types of sauces. Explain how this is possible?(3C)

                    10. What are two patterns that you can find in Pascal’s Triangle (2C)

                    11.  Find the expansion of  (3C)

                    12. We need to make a six-person team from a group of twenty; 8 boys and 12 girls. What is the total number of ways we can select a team if:

                    a) We want exactly 3 boys (1T)

                    b) We want at least 1 girl (1T)

                    c) We want 4 girls but one of them is Chiara (2T)

                    d) We want at least 1 boy or 1 girl (2T) 

13. My brother has 8 pictures of me and 6 of my brother that she wants to place on a fire place in a line. She wants to pick 4 pictures of me and 3 of my brother. If she wants to place alternating pictures, how many ways can we do it (2T)


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