Product Rule for Counting Flashcards

All 6 cards in this deck

State the product rule for counting.

If there are $m$ ways of doing one task and $n$ ways of doing another, there are $m \times n$ ways of doing both.

How do you find the number of ways of making three independent choices?

e.g. 16 shirts, 5 pairs of jeans, 3 jackets

Multiply all three numbers together.
$16 \times 5 \times 3 = 240$ outfits

What are the steps to use the product rule in reverse to find a missing number of options?

e.g. 5 starters, 8 mains and some desserts give 240 meals

1. Multiply the known choices: $5 \times 8 = 40$
2. Divide the total by this: $240 \div 40 = 6$
3. There are 6 desserts

When a problem offers alternative combinations joined by 'or', what do you do with the separate products?

Add them together.
e.g. (starter and main) or (main and dessert) gives $9 \times 15 + 15 \times 8$

True or false? If dividing a total by the known number of choices gives a decimal, the claimed total is impossible.

True. The number of options must be a whole number, so the claim cannot be correct.

How many matches are played if each of $n$ teams plays every other team once?

$\dfrac{n(n-1)}{2}$
e.g. 10 teams give $\frac{10 \times 9}{2} = 45$ matches.