math

A box contains 8 red marbles, 8 green marbles, and 10 black marbles. A sample of 12 marbles is to be picked from the box. How many samples contain exactly 7 red marbles or exactly 6 green marbles?

The answer key sets it up as (8 nCr 7)*(18 nCr 5)+(8 nCr 6)*(18 nCr 6)=588,336. Where does the (18 nCr 5) and (18 nCr 6) come from?

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asked by Dan
  1. 18 marbles are not red
    ... 5 of those are the remainder of the 12 marbles picked

    18 marbles are not green
    ... 6 of those are the remainder of the 12 marbles picked

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    posted by scott

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