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? Select the correct option:
A) 100	B) 40	C) 66	D) 80	E) 75

Rationale: two ways . . . 1 ) total ways = 10 c 3 = 10 ! / 7 ! 3 ! = 120 . . ways without python developer = 6 c 3 = 6 ! / 3 ! 3 ! = 20 . . ways of at least one python developer = 120 - 20 = 100 . . 2 ) ways of selecting only one = 4 * 6 c 2 = 4 * 15 = 60 . . ways of selecting only two = 4 c 2 * 6 c 1 = 6 * 6 = 36 . . ways of selecting all three = 4 c 3 = 4 = 4 . . total = 60 + 36 + 4 = 100 . . . answer : a
Answer: A