Addition & Multiplication Principles (Ex 10A)

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

Name

Class

Date

Learning intentions.

Use the multiplication principle for a sequence of choices ("and" → ×)
Use the addition principle for a choice between separate options ("or" → +)
Combine both rules and choose the right one for each step

Key results

Multiplication ("and"): a sequence of stages with $m$, then $n$, … options has $m\times n\times\cdots$ outcomes. Addition ("or"): a choice between separate, non-overlapping groups of $m$ and $n$ options gives $m+n$.

Warm-up — and or or?

1. For each, write × (multiply) or + (add), then give the answer.

a Toss a coin and roll a die: outcomes

b Travel by one of $3$ buses or one of $2$ trains: ways

c A shirt (from $5$) and a tie (from $4$): outfits

d Order one of $6$ mains or one of $4$ light meals: orders

Part A — Multiplication principle

2. A café meal is one entrée (from $3$), one main (from $5$) and one dessert (from $2$). Fill the boxes, then find the total number of meals.

3. A 4-digit PIN uses digits $0$–$9$ and digits may repeat.

a How many PINs?

b How many if no digit may repeat?

4. A code is $2$ letters ($A$–$Z$) followed by $4$ digits ($0$–$9$), repeats allowed. How many codes are possible? (Leave your answer as a product, then evaluate.)

Part B — Addition principle

5. A library lets you borrow one item today: a novel (from $12$), a graphic novel (from $7$) or a magazine (from $5$). How many choices of single item?

6. Explain in one sentence why we add in Q5 but multiply in Q2.

Counting 10A — continued

Part C (combining both principles) · Challenge

Name

Part C — Combining both principles

7. At a kiosk you choose a drink (from $4$) and a snack, where the snack is a pie (from $6$) or a salad (from $3$).

a Number of snack choices

b Number of drink-and-snack combos

8. A meal deal is a drink (from $3$) and a main, where the main is a burger (from $4$) or a wrap (from $2$). How many deals are possible?

9. An ice-cream is built from a cone (from $3$), a flavour (from $8$) and a topping (from $2$).

a How many ice-creams?

b How many if you may have no topping as well (so $3$ topping options)?

10. A restaurant lets you order a two-course meal that is either (a starter and a main) or (a main and a dessert). There are $2$ starters, $3$ mains and $2$ desserts. How many two-course meals are possible?

Challenge

11. Victorian number plates: the old system was $3$ letters then $3$ digits; the new system is a digit, then $2$ letters, then a digit, then $2$ letters (repeats allowed throughout).

a How many old plates were possible?

b How many new plates are possible?

c Which system gives more plates, and roughly how many times more?