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1 temporary employee in each office

So after giving each office 1 employee, there are remaining 2 employees.

Now we have to distribute 2 employee in 4 offices

$O_{1}$         $O_{2}$         $O_{3}$          $O_{4}$

   2                      0                   0                 0

   0                      2                    0                0

   0                      0                    2                0

   0                      0                    0                2

   1                      1                     0                0

   1                      0                     1                 0

   1                      0                      0                1

    0                     1                      1                 0

    0                      1                      0                 1

    0                       0                     1                  1

 

So, in 10 ways
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Let employees in office i = Oi

Therefore : O1 + O2 +O3+ O4 = 6  where Oi>=1

Putting at least 1  employee in each office we are left with (Oi complement = oi)

o1 + o2 +o3+ o4 = 6 - 4  where oi>=0

o1 + o2 +o3+ o4 = 2

thus using combinations with repetition we have ( n +r -1 , r)

n=4, r=2

( 4 + 2 - 1 , 2 ) = (5,2) = 10 ways

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