Question 1153867: There are 10 pcs of fruit, 6 were pears. If worker randomly selects 3 pcs for a basket, what is the probability that all were pears?
Answer by ikleyn(52903)   (Show Source):
You can put this solution on YOUR website! .
There are two ways to solve this problem.
One way is to use the formula P =  . (1)
The denominator of this formula,  , is the number of combinations of 10 items taken 3 at a time.
In other words, it is the number of all triples that can be formed from 10 pieces of fruits.
The numerator,  , is the number of all triples of pears that can be formed of 6 pears.
=  = 120.
=  = 20.
Therefore, the probability under the question is P =  =  .
Another way is to write
P =  = simplifying =  =  = , (2)
which leads to the same answer.
In formula (2), first factor  is the probability to get one pear from 10 fruits;
the factor  is the probability to get second pear from the remaining 9 fruits;
and the last factor  is the probability to get third pear from the remaining 8 fruits;.
So, the problem can be solved by any of these two ways, and you should know both.
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