D(2)= 1

D(3)=2

D(4)=9

D(5)=44

D(6)=265

D(7)= 1854

Conclusion of dislocation rearrangement:

If there are n objects, then the number of dislocations and rearrangements is represented by Dn. What you need to know is:

D2= 1，D3=2，D4=9，D5=44。

The characteristics of dislocation rearrangement are still obvious. For example, four chefs have cooked four dishes. How many ways can each chef not eat his own cooking? This is a dislocation rearrangement of three elements, not a dislocation rearrangement of six elements.

For example, there are four envelopes corresponding to four letters, and how many ways each letter does not contain its own envelope is the dislocation and rearrangement of four elements; There are five couples going to dance and changing partners. How many ways can a partner differ from a spouse, that is, the dislocation and rearrangement of the five elements?

Extended data:

The expression is: n letters numbered 1, 2, n, and n envelopes numbered 1, 2, n. Each letter and envelope are required to have a different number. The installation method is as follows:

This kind of problem has a fixed recurrence formula. If the number of dislocations of n letters is Dn, then D 1=0, D2= 1,

Dn = (n- 1) (dn-2+dn-1) where n-2 and n-1are subscripts.

n & gt2

Just remember the first few items of Dn: D 1=0, D2= 1, D3=2, D4=9, D5=44. We just need to remember the conclusion and make a calculation.

Reference source: Baidu Encyclopedia-Dislocation rearrangement