5 + 1 Dual Chamber Number Picker (69/26): How to use this preset
What the selection means
This 69/26 format picks five main entries and one secondary entry. The secondary pool supplies one instruction for the whole selection, rather than another main item. Main and secondary numbers may have the same value because the chambers are independent.
Using the controls
Choose the number of sets and a tumble time, then press Pick Numbers. Read the main and secondary results separately. Switching between selection order and sorted order changes the display, not which balls were picked. Each new set refills both chambers.
An activity to try
Number 69 discussion prompts and 26 ways of responding. A response card might ask for a sketch, a short explanation or an example. Use the five main numbers to find the prompts and the secondary number to choose the response style for the round. Keep the two numbered lists visibly labelled.
Create your own version with PhysPicks
Set the number range and pick count for each chamber to build a two-part game, such as prompts and instructions.
Create a dual-chamber gameWhat are the probabilities?
These calculations assume uniform selection without replacement within each pool and independent chambers. They describe a mathematical model, not measured or certified probabilities for the PhysPicks physics simulation.
| Event defined before the selection | Theoretical probability |
|---|---|
| One specified main number is the first ball out | 1/69 ≈ 1.45% |
| One specified main number appears anywhere in the completed set | 5/69 ≈ 7.25% |
| Exactly one of your 5 preselected main numbers matches (secondary pool ignored) | 3,176,880/11,238,513 ≈ 28.27% |
| One specified secondary number appears in the secondary selection | 1/26 ≈ 3.85% |
| One specified complete combination, ignoring order | 1/292,201,338 |
C(69,5) × C(26,1) = 292,201,338
For k picks from n numbers, a specified number is included with probability k/n. There are C(n,k) = n! / (k!(n−k)!) unordered sets. With two independent pools, multiply their combination counts. “One specified number appears” is different from “exactly one of my chosen numbers matches”. A previous result does not make a number due next time.
P(X = 1) = C(5,1) × C(64,4) / C(69,5)