Solution
Ten People, Five Pairs
Show the problem again
In how many ways can 10 people be divided into 5 pairs? The pairs are unlabelled: only who is paired with whom matters. Give an integer.
Worked solution
The answer is 945. Take the person with the smallest label; their partner can be chosen in 9 ways. Among the remaining 8, the smallest-labelled person has 7 possible partners, and so on. The total is 9 × 7 × 5 × 3 × 1 = 945. Equivalently, 10!/(2⁵ · 5!) = 3,628,800/3840 = 945, dividing out the order inside each pair and the order of the pairs.
Source: Classic counting exercise in wide circulation; no traceable original source. Statement written for AxiomIQ.