96
Non-standard problems (listing options)
Textbook Part 3, pp. 46–47
GoalFind how many ways there are by listing every option in an orderly way.
New words
option · variantway · usulto choose · tanlamoq
Explanation
Some problems ask “how many ways are there?”. To solve them, list every option in order, making sure not to miss or repeat any. For example: apple (A) or orange (O) juice with meat (M) or potato (P) samsa: AM, AP, OM, OP — 4 ways.
Worked examples
4 cups on a table (1, 2, 3, 4). Choosing 2: 12, 13, 14, 23, 24, 34 — 6 ways.
6 of 7 tables are taken and 1 is empty. The empty one could be any of them — 7 ways.
Class activity
Outfit combinations: pictures of 2 shirts and 3 pairs of trousers. Children draw every pair and count the outfits (6).
Practice
1
Juice: A or O. Samsa: M or P. List all the pairs.
AM, AP, OM, OP — 4
2
There are 3 buses. The leader can ride any one. How many choices?
3
3
How many two-digit numbers can you make from 1, 2, 3 without repeating a digit?
6: 12, 13, 21, 23, 31, 32
4
There are 2 roads from A to B and 2 from B to C. How many routes from A to C?
4