In a certain group of 10 developers, 4 developers code only in Python and the rest program in either Ruby on Rails or PHP - but not both. If a developer organization is to choose a 3-member team, which must have at least 1 developer who codes in Python, how many different programming teams can be chosen? Choose the correct option:
A) 100 B) 40 C) 66 D) 80 E) 75
Two ways...   1) total ways = 10C3 = 10!/7!3! = 120..   ways without python developer = 6C3= 6!/3!3!=20..   ways of at least ONE python developer = 120-20 =100..   2) ways of selecting ONLY one = 4*6C2 = 4*15 = 60..   ways of selecting ONLY two = 4C2*6C1 = 6*6 = 36..   ways of selecting all three = 4C3 = 4 = 4..   Total = 60+36+4=100...   100NSWER:100
<result>A</result>
In a certain group of 10 developers, 4 developers code only in Python and the rest program in either Ruby on Rails or PHP - but not both. If a developer organization is to choose a 3-member team, which must have at least 1 developer who codes in Python, how many different programming teams can be chosen?