Systematic Lists Flashcards

All 5 cards in this deck

What does it mean to write a systematic list?

Listing outcomes in a fixed order so that none are missed or repeated.

What are the steps to list all possible outcomes systematically?

e.g. all two-digit numbers made from the digits 1, 2, 3 with no repeats

1. Fix the first digit as the smallest and list the rest in order: 12, 13
2. Repeat with each other first digit: 21, 23, then 31, 32
3. Count the list: 6 outcomes

When listing combinations of one item from each of two sets, how do you keep the list systematic?

Keep the first item fixed while you list every choice of the second, then move on.
e.g. AX, AY, BX, BY

True or false? When listing pairs where the order does not matter, AB and BA should both be written down.

False. If order does not matter they are the same pair, so list it once.

How can the product rule be used to check a systematic list is complete?

Multiply the numbers of choices and compare with how many items you listed.
e.g. 3 tops and 2 hats should give $3 \times 2 = 6$ outfits.