Work through the levels in order. Type your answer and press Check — open the worked solution if you get stuck. Answers like -6, 3/4 or 0.25 are typed exactly as shown. A ⭐ Bonus Challenge at the end is extra credit — skip it if the rest was hard work.
Level 1 · Warm-up
1 A three-digit code uses digits 0–9 and repeats are allowed. How many codes are possible?
Show worked solution
10 × 10 × 10 = 1000.
2 Three different books are arranged on a shelf. Write the number of choices for the first position, and the total number of arrangements.
Show worked solution
There are 3 choices for the first position, then 2, then 1, giving 3 × 2 × 1 = 6 arrangements.
3 One raffle ticket wins out of 250 sold. If you hold one ticket, what number goes in "1 in ___" for your chance of winning?
Show worked solution
One winner out of 250 possible tickets, so 1 in 250.
Level 2 · Core
4 A code is a letter from A–E followed by one digit 0–9. Repeats do not apply. How many codes are possible?
Show worked solution
5 × 10 = 50.
5 Four different cards are dealt in a row. Write the number of arrangements, and the chance of one particular order coming up (as the number in "1 in ___").
Show worked solution
There are 24 arrangements, so one particular order has a chance of 1 in 24.
6 A bag holds 12 counters and 3 are red. Simplify the chance of drawing red to "1 in ___". What number goes in the blank?
Show worked solution
3 in 12 simplifies to 1 in 4.
Level 3 · Challenge
7 A lock uses two digits 0–9 followed by one letter A–D, with repeats allowed.1 There are 400 possible codes.
2 There are 24 possible codes.
3 The chance of guessing correctly first time is 1 in 400.
Which statements are correct?
2 There are 24 possible codes.
3 The chance of guessing correctly first time is 1 in 400.
Which statements are correct?
Show worked solution
10 × 10 × 4 = 400 (1 ✓, 2 ✗), and one correct code out of 400 is a chance of 1 in 400 (3 ✓). 1 and 3.
8 The digits 2, 5, 7 and 9 are used once each to make a four-digit number. Write the total number of arrangements, and how many of them start with 9.
Show worked solution
Altogether 4 × 3 × 2 × 1 = 24. Fixing 9 first leaves 3 × 2 × 1 = 6 arrangements.
9 A four-digit code uses digits 0–9 with repeats allowed. How many times more likely is a correct guess if you already know the four digits used but not their order? Give your answer to the nearest whole number.
Show worked solution
10 000 ÷ 24 = 416.6…, so about 417 times more likely.