There are 7 rotten apples in a crate of 26 apples. How many samples of 3 apples can be drawn from the crate? How many samples of 3 could be drawn in which all 3 are rotten? How many samples of 3 could be drawn in which there are two good apples and one rotten apple?
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How many samples of 3 apples can be drawn from the crate?
you have 26 apples in total so you can choose 3 apples from 26 in 26C3 ways...i.e 26 combination 3 ways...i.e. 2600...
How many samples of 3 can be drawn in which all 3 are rotten?
there are 7 rotten apples in total...so one can choose 3 rotten apples from 7 in 7C3 ways...7 combination 3 ways...ie 35 ways...
How many samples of 3 can be drawn in which there are 2 good apples and one rotten apple?
one wishes to choose 3 apples in total from a total of 27...out of that 26, 7 are rotten...How many ways can he choose 2 good AND 1 bad apple:
since there are 7 rotten apples, there are 19 good apples thus one can choose 2 good apples from 19 in 19C2...and one can choose 1 bad apple from 7 in 7C1...so one can choose 2 good and 1 rotten apple in 19C2 x 7C1 = 171 x7 = 1197 ways or samples