No matter the two grouping methods (22 1 or 3 1 1), there will be some duplication. For example, 3 1 1: Take three first, and the remaining two are actually only 1. If calculated by C (2, 1), it will become. So divide by a (2 2,2).

Similarly, in 22 1, the grouping of two "2" is the same. For example, five people are: abcde, the first group: take ab first, then cd, then E; The second group: take cd first, then ad, then E; In fact, the two are the same, so it needs to be divided by a (2 2,2).

For 3 1 1, it can actually be simpler and more direct:

c(5，3)*a( 3，3)，

Because three are taken away, only two are left, which are automatically divided into two groups without calculation. Then these three groups can be rearranged.

The same is true of 22 1. Take 1 first, the remaining four, and then take two:

C(5， 1)C(4，2)A(3，3)