A certain team consists of 4 professors and 6 teaching assistants. How many different teams of 3 can be formed in which at least one member of the group is a professor? (Two groups are considered different if at least one group member is different.) Choose the correct choice
A) 48
B) 100
C) 120
D) 288
E) 600
The groups can be formed as   PTT + PPT + PPP where P=professor and T=Teaching assistant   Number of different teams of 3 can be formed in which at least one member of the group is a professor   = 4C1* 6C2 + 4C2*6C1 + 4C3   = 4!/3! * 6*5/2 + 4*3/2 * 6 + 4   =60 +36 + 4   4 /3  * 6*5/2 + 4*3/2 * 6 + 4= 
<gadget id="calculator">4 /3  * 6*5/2 + 4*3/2 * 6 + 4</gadget>
<output>60</output>
60 +36 + 4= 
<gadget id="calculator">60 +36 + 4</gadget>
<output>100</output>
100   Answer 100
<result>B</result>
A certain team consists of 4 professors and 6 teaching assistants. How many different teams of 3 can be formed in which at least one member of the group is a professor? (Two groups are considered different if at least one group member is different.)