Worksheets · Foundation and Higher

Systematic lists and combinations

3 exam-style questions. Answers and the mark for each step are on the last page.

Question 1Non-calculator · 3 marks
A café sells three kinds of sandwich: cheese (C), ham (H) and egg (E). It sells two drinks: tea (T) and juice (J). Lucy buys one sandwich and one drink.
(a) List all the possible combinations Lucy could buy. (2)
(b) How many different combinations are there? (1)
Question 2Non-calculator · 4 marks
Use two different digits from 1, 2, 4, 6, 8 to form a two-digit number.
(a) How many of the numbers are even? (2)
(b) How many of the numbers are odd? (2)
Question 3Non-calculator · 5 marks
Three positive whole numbers add up to $12$ . The order does not matter, so $2 + 3 + 7$ and $7 + 2 + 3$ count as the same set.
(a) Work out how many different sets of three numbers there are. (3)
(b) Three sticks have these whole-number lengths, in cm, and are used as the sides of a triangle. For how many of the sets from part (a) can a triangle be made? (2)

Answers and marks

(a) CT, CJ, HT, HJ, ET, EJ

(b) $6$

(a) $16$

(b) $4$

(a) $12$

P1 A systematic method: writing each set in decreasing order and working down from the largest first number.
P1 At least eight correct sets with no repeats.
A1 The correct answer, $12$ .

(b) $3$

P1 Using the triangle condition, largest side less than the sum of the other two (so less than 6).
A1 The correct answer, $3$ .

Systematic lists and combinations

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