A plant manager must assign 12 new workers to one of five shifts. She needs a first, second, and third shift, and two alternate shifts. Each of the shifts will receive 2 new workers. How many different ways can she assign the new workers?  Choose the correct choice from the following choices:
A) 23760  B) 47520  C) 33000  D) 48600  E) 54000
whatever : my take selecting team of 2 out of 12 to assign to the shifts = 12C2 = 66 ways.   now 2 out of 12 means total of 6 group possible.   so putting them in shifts = counting methode: first, second, third, alt , alt   = 6*5*4*3*2*1= 
<gadget id="calculator">6*5*4*3*2*1</gadget>
<output>720</output>
720   here alt and alt are the same: so  720/2= 
<gadget id="calculator"> 720/2</gadget>
<output>360</output>
360 ways.   total ways of selecting= (selecting 2 out of 12)*arranging those teams in shifts   = 66*360= 
<gadget id="calculator">66*360</gadget>
<output>23_760</output>
23760   23760ns: 23760
<result>A</result>
A plant manager must assign 12 new workers to one of five shifts. She needs a first, second, and third shift, and two alternate shifts. Each of the shifts will receive 2 new workers. How many different ways can she assign the new workers?