In a group of 10 doctors, 3 doctors are only pediatricians; the others are surgeons or general practitioners - but not both. A team of 3 doctors is to be chosen which must have at least 1 pediatrician, how many different teams can be chosen?	Choose the correct option:
A) 85 B) 140 C) 60 D) 80 E) 75
The problem asks for a combination, since order doesn't matter. Now, selecting r items from a set of n gives the Combination Formula: nCr= n!/r!(n-r)!   n = 10   r = 3   So, total teams is 10C3 = 10!/(3!(10 - 3)!) = 120, and   n = 10 - 3= 
<gadget id="calculator">10 - 3</gadget>
<output>7</output>
7   r= 3   for teams without a pediatrician is 7C3 = 7!/(3!(7 - 3)!) = 35,   so, teams with at least 1 pediatrician = 120 - 35= 
<gadget id="calculator">120 - 35</gadget>
<output>85</output>
85   85nswer: 85
<result>A</result>
In a group of 10 doctors, 3 doctors are only pediatricians; the others are surgeons or general practitioners - but not both. A team of 3 doctors is to be chosen which must have at least 1 pediatrician, how many different teams can be chosen?