Answer:
13,749,310,575
Explanation:
You want to know the number of ways 22 children in a class can be paired up for a field trip.
Pairs
One way to form pairs is to have the children line up, then have each odd-numbered person pair with the next higher even numbered person.
The number of ways the children can line up is 22!. Since any of the 11 pairs can be in that line in either order, we must divide that number by (2!)^11. Further, since those 11 pairs can appear in line in any order, we must further divide the number by 11!.
The number of ways the children can be paired is ...
22!/(2^11 · 11!) = 13,749,310,575 . . . . . possible pairings
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Additional comment
The mathematical description of this number of pairs is ...
a(11) = (2·11 -1)!! = 1·3·5·7·...·21 . . . . . . the "double factorial"
It looks like this could be considered as the product of the numbers of different partners each "next" child could have. That is, the first child could have any of 21 partners. The next child could have any of 19 partners, and so on.
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