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Math problem: Six college students apply to three employers. If each unit employs at least one person, how many different employment methods are there?
Answer:

Can be classified and solved.

(1) 6 people were admitted.

Can be divided into three categories.

① 4+ 1+ 1,C(6,2)*A(3,3)= 15*6=90

② 3+2+ 1,C(6,3)C(3,2)*C( 1, 1)*A(3,3)=360

③ 2+2+2 C(6,2)*C(4,2)*C(2,2)/A(3,3) *A(3,3)=90

There are 540 such cases.

(2) Admission of 5 people.

Choose five people first, c (6,5) = 6.

And then divided into two categories.

① 3+ 1+ 1,C(5,3)*A(3,3)= 10*6=60

② 2+2+ 1,C(5,2)C(3,2)*C( 1, 1)/A(2,2) *A(3,3)=90

In this case, there are 150*6=900 kinds of * *.

(3) admit 4 people.

Choose four people first, c (6,4) =15.

And then divided into one category.

① 2+ 1+ 1,C(4,2)*A(3,3)=6*6=36

In this case, there are 15*36=540 * *.

(4) admit three people.

Choose three people first, c (6,3) = 20.

And then divided into one category.

① 1+ 1+ 1,A(3,3)=6

In this case, * * has 20*6= 120.

Based on the principle of classified counting,

* * * There are 540+900+540+120 = 2100 species.