Try it on paper first. A hint, the key idea and the worked solution are here when you need them.
Without running anything, say how many subsets there are for lists of 5, 10 and 20 items. Then say how many arrangements there are for texts of 5 and 8 letters (with no repeated letters). Check the small ones with a program.
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Plan. Each item is in or out, so a list of items has subsets. The arrangements of different letters are .
| Subsets | Arrangements | |
|---|---|---|
| 5 | 32 | 120 |
| 8 | 256 | 40 320 |
| 10 | 1 024 | 3 628 800 |
| 20 | 1 048 576 | about |
For 5 and 10 items the subsets are 32 and 1024. For 20 items, 1 048 576. The arrangements: 120 for 5 letters, 40 320 for 8 letters.
Check with a program.
The program shows 32 32, and then 120 40320.
Answer: 32, 1024 and 1 048 576 subsets. 120 and 40 320 arrangements.
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