Stage 8 - Q1 - 2 marks
A badge uses one letter, X or Y, and one symbol, circle, square or triangle. How many badges are possible?
Hint
List three symbols for each letter.
Stage 8 - Q2 - 2 marks
List all two-letter codes made from A, B and C without repeating a letter.
Hint
AB and BA are different codes.
Stage 8 - Q3 - 3 marks
A two-letter code uses one of P, Q, R followed by one of P, Q, R. Repetition is allowed. How many codes contain two different letters?
Hint
Count all codes, then remove the three repeats.
Stage 8 - Q4 - 3 marks
Use two different cards from 0, 3 and 8 to make a two-digit number. List every valid number.
Hint
Zero is allowed in the units place, but not the tens place.
Stage 8 - Q5 - 3 marks
A valid two-digit number from different cards 0, 3 and 8 is selected uniformly. Find the probability that it is even.
Hint
Check the final digit of each valid number.
Stage 8 - Q6 - 4 marks
Cards 2, 5 and 9 are put in a random order to form a three-digit number. List the outcomes beginning with 5 and find their probability.
Hint
After fixing the first card, the other two can swap.
Stage 8 - Q7 - 4 marks
A password has two different letters from A, B, C, D followed by a digit 1, 2 or 3. How many passwords are possible?
Hint
The second-letter choice has one fewer option.
Stage 8 - Q8 - 4 marks
Three different cards from 1, 2, 4 and 7 form a three-digit number. Find the probability of an odd number when all valid arrangements are equally likely.
Hint
Fix the units digit first for this event.
Stage 8 - Q9 - 5 marks
Three different cards from 0, 1, 2 and 4 form a three-digit number, with no leading zero. How many numbers are even? Explain how zero changes the count.
Hint
Treat a zero units digit separately from the other even units digits.
Stage 8 - Q10 - 6 marks
Three different cards from 0, 2, 5 and 7 form a three-digit number with no leading zero. All valid numbers are equally likely. Find the probability of a multiple of five.
Hint
Separate the two possible final digits and check the leading digit in each case.