A certain company assigns employees to offices in such a way that some of the offices can be empty and more than one employee can be assigned to an office. In how many ways can the company assign 3 employees to 2 different offices?
A. 5
B. 6
C. 7
D. 8
E. 9
Perm & Comb
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3 people to fill 2 placescsandeepreddy wrote:A certain company assigns employees to offices in such a way that some of the offices can be empty and more than one employee can be assigned to an office. In how many ways can the company assign 3 employees to 2 different offices?
A. 5
B. 6
C. 7
D. 8
E. 9
must be 3P2 = 6 not sure though. Whats the OA ?
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We clould also do the above as follows
2 offices
3 employess
case1 0 in first office and 3 in the other this can be done in 2 ways
case2 2 in first office and 1 in the other this can be done in 3C2*2C1=6
So total ways= 2+6=8
2 offices
3 employess
case1 0 in first office and 3 in the other this can be done in 2 ways
case2 2 in first office and 1 in the other this can be done in 3C2*2C1=6
So total ways= 2+6=8
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You can also think like:
Every office has three chairs. So we can 3,2,1, or NOBODY sitting on them = 4 options for each office. We have 2 office; so the answer is 8.
Every office has three chairs. So we can 3,2,1, or NOBODY sitting on them = 4 options for each office. We have 2 office; so the answer is 8.
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But you can't have nobody and nobody so this isn't correct.logitech wrote:You can also think like:
Every office has three chairs. So we can 3,2,1, or NOBODY sitting on them = 4 options for each office. We have 2 office; so the answer is 8.
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let ABC be 3 people
total arrangements: (ABC), (ACB), (BCA) =3*2=6
(ABC0) = 1*2=2
TOTAL 6+2=8
total arrangements: (ABC), (ACB), (BCA) =3*2=6
(ABC0) = 1*2=2
TOTAL 6+2=8