How many pairs of ticks exist? - briefly
If only two ticks are present, exactly one pair can be formed. For n ticks, the number of distinct pairs equals n × (n − 1) ⁄ 2.
How many pairs of ticks exist? - in detail
The problem concerns determining the count of distinct tick pairs that can be formed from a collection of tick marks.
If the set contains n individual ticks, the number of unordered pairs equals the binomial coefficient
- C(n, 2) = n · (n – 1) ⁄ 2.
This formula follows from choosing two elements without regard to order. For example, with 5 ticks the calculation yields 5 · 4 ⁄ 2 = 10 distinct pairs.
When order matters, each tick can serve as the first element of a pair and any tick, including itself, can be the second element. The count of ordered pairs is therefore
- n · n = n².
If self‑pairing is excluded, the ordered count reduces to
- n · (n – 1).
Special cases:
- n = 0 → no pairs (both unordered and ordered counts are zero).
- n = 1 → unordered pairs = 0; ordered pairs = 1 if self‑pairing allowed, otherwise 0.
The formulas apply universally, whether the ticks represent time stamps, graphical markers, or any discrete items labeled as ticks. The calculation requires only the total quantity of ticks; no additional properties influence the pair count.