Question

A bag contains 9 apples and 7 oranges. If you select 8 pieces of fruit without looking, how many ways can you get exactly 7 apples?

Answer 1

you are asked how many ways to choose 7 apples and one orange right?

Answer 2

yes

Answer 3

evidently there are 7 ways to get one orange

Answer 4

as for the apples, you are asked how many ways to choose 7 out of 9, i.e. "nine choose seven" written as \[\binom{9}{7}\] or sometimes \[_9C_7\]

Answer 5

compute as \[\binom{9}{7}=\binom{9}{2}=\frac{9\times 8}{2}\]

Answer 6

I thought I would 16/9 * 15/8 then so on and so on

Answer 7

are you looking for a probability ( a fraction) , or the number of ways to do something (a whole number) ?

Answer 8

a whole number

Answer 9

ok good that is what i thought, so no fractions there just \[\frac{9\times 8}{2}=9\times 4=36\] for the seven out of nine apples times the 8 for one out of 8 oranges