duongthang wrote:a certain company assigns employees to offices in such a way that some of the officies can be empty and more than one employee can be assigned to an office. in howmany ways can the company assign 3 employees to 2 different offices.

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this is a good question from 15 test set and so needs to study.

Lets say:

We have offices A and B
We have three employees: x, y and z

1. We can have all three employees in Office A and none in Office B:

No of ways = 1 (all three in A)

2. We can have two employees in Office A and one employee in Office B:

No of ways = 3 (x,y in A, z in B) OR (x,z in A, y in B) OR (y,z in A, x in B)

3. We can have one employee in Office A and two employees in Office B:

No of ways = 3 (x,y in B, z in A) OR (x,z in B, y in A) OR (y,z in B, x in A)

4. We can have all three employees in Office B and none in Office A:

No of ways = 1 (all three in B)


So in total, we have 1 + 3 + 3 + 1 = 8 different ways

Choose D.

-BM-