SOLUTION: A bag contains 8 apples and 6 oranges. If you select 7 pieces of fruit without looking, how many ways can you get exactly 6 apples? Can you please show me how to work this problem

Question 597772: A bag contains 8 apples and 6 oranges. If you select 7 pieces of fruit without looking, how many ways can you get exactly 6 apples?
Can you please show me how to work this problem.... I think it is 8!/6! = 56???
Found 2 solutions by scott8148, jim_thompson5910:
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
there are 8C6 ways of selecting 6 apples out of 8

there are 6 ways of selecting one orange out of 6, to go with the 6 apples

8C6 * 6 = (8 * 7 / 2) * 6 = 168
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
If you have 7 selections, and 6 of them are taken up by apples, then the last selection must be an orange.

There are 8 apples. So there are 8 C 6 = (8!)/(6!(8-6)!) = 28 ways to select 6 apples (from 8)

There are 6 oranges. Since the there's only one spot for an orange, there are only 6 ways to select an orange.

So multiply these results to get 28*6 = 168

This means that there are 168 ways to select exactly 6 apples.
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