Solutions — Counting 10A Worksheet

Year 11 Mathematical Methods · Cambridge Methods 1&2, Counting Methods · Mr Wong

ANSWER KEY

Warm-up — and or or?

Q1. Operation, then value:

a × : $2\times6=12$

b + : $3+2=5$

c × : $5\times4=20$

d + : $6+4=10$

Part A — Multiplication principle

2 $3\times5\times2=30$ meals (boxes: 3, 5, 2)

3a $10^4=10\,000$ PINs

3b $10\times9\times8\times7=5040$ (no repeats)

4 $26^2\times10^4=6\,760\,000$ codes

Part B — Addition principle

5 $12+7+5=24$ choices

6 In Q5 you pick one item from separate groups (an "or") so the counts add; in Q2 you pick one from each course in sequence (an "and") so the counts multiply.

Part C — Combining both principles

7a $6+3=9$ snacks

7b $4\times9=36$ combos

8 $3\times(4+2)=18$ deals

9a $3\times8\times2=48$ ice-creams

9b $3\times8\times3=72$ (3 topping options)

10 $(2\times3)+(3\times2)=6+6=12$ (starter+main) or (main+dessert)

Challenge

11a $26^3\times10^3=17\,576\,000$ old plates

11b $10\times26^2\times10\times26^2=10^2\times26^4=45\,697\,600$ new plates

11c The new system gives more — about $2.6$ times as many ($45\,697\,600 \div 17\,576\,000 \approx 2.6$).