Question 477438
"A box contains 7 red cards, 6 white cards and 4 blue cards. How many selections of three cards can be made so that 
a) all three are red, 
Easiest Way:
# of ways to get 3 red: 7C3 = (7*6*5)/(1*2*3) = 35
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b) none are red?
Easiest Way:
# of ways to get 3 not red: 10C3 = (10*9*8)/(1*2*3) = 120
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Your Question::::::
17C3 - 7C3 = 680-35 = 645 
The 645 includes all the combinations that allow
1 red in the group of 3 or 2 reds in the group of 3.
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Your 35 is the # of groups with ALL red
Your 120 is the # of groups with NO red
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Cheers,
Stan H.