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- 1. Multiple Choice
Gloria and Bob and five other people walk through a doorway one at a time. In how many ways can the seven people go through the doorway if Bob goes through the doorway after Gloria?
- 2. Multiple Choice
A child arranges 5 blocks in a row. Two blocks are painted blue, one is painted red, one is painted green and one is painted white. How many possible patterns of colours are there if the two blue blocks are next to one another?
- 3. Multiple Choice
Mr and Mrs Brown and their four children go to the cinema. They are randomly allocated six adjacent seats in a single row. What is the probability that the four children are allocated seats next to each other?
- 4. Multiple Choice
How many arrangements can be made using all the letters of the word ISOSCELES?
- 5. Multiple Choice
Seven people are seated at a round table. What is the probability that two people, Jenny and Lindsay, do not sit next to one another?
- 6. Multiple Choice
Three cards are selected at random from a standard pack of 52 cards.
What is the probability that at least two of them are clubs?
- 7. Multiple Choice
The staff in an office consists of 4 females and 7 males.
What is the probability that a randomly chosen committee of 5 staff will contain exactly 3 males?
- 8. Multiple Choice
- 9. Multiple Choice
A fair, six-sided die is thrown seven times. What is the probability, correct to three decimal places, that a ‘3’ occurs on exactly two of the seven throws?
- 10. Multiple Choice
A pair of fair dice is tossed eight times. What is the probability, correct to three decimal places, of getting a sum of 9 on at least two occasions?
- 11. Multiple Choice
A group of 37 mountain hikers were travelling into the mountain ranges when a storm suddenly broke out. All the hikers rushed into 6 caves for cover. Which of the following statements are true if all the hikers picked their cave at random? Note all caves have more than enough space to hold everyone.
There will always be 1 cave that has no people.
There will be at most two caves with at least 8 people.
There will be at least one cave with at least 7 people.
There will be at least one cave with at most 5 people.
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