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?

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