A firm is divided into four departments, each of which contains four people. If a project is to be assigned to a team of three people, none of which can be from the same department,what is the greatest number of distinct teams to which the project could be assigned?
Choose the correct choice from the following answers: A) 4^3 B) 4^4 C) 4^5 D) 6(4^4) E) 4(3^6)
First member: 4*4= 
<gadget id="calculator">4*4</gadget>
<output>16</output>
16 choices;   Second member: 4*3= 
<gadget id="calculator">4*3</gadget>
<output>12</output>
12 choices (as one department already provided with a member);   Third member: 4*2= 
<gadget id="calculator">4*2</gadget>
<output>8</output>
8 choices (as two departments already provided with members);   So, we have: 16*12*8.   Since the order of the members in a team does not matter (we don't actually have 1st, 2nd and 3rd members) then we should divide above by 3! to get rid of duplication: 16*12*8/3!=4^4.   ANSWER:4^4
<result>B</result>
A firm is divided into four departments, each of which contains four people. If a project is to be assigned to a team of three people, none of which can be from the same department,what is the greatest number of distinct teams to which the project could be assigned?