1. ## probability

a basket has 3 oranges 4 apples & 3 MANGOES. IN HOW MANY WAYS 2 FRUITS CAN BE CHOSEN FROM THE BASKET ? HOW MANY OF THEM WILL CONTAIN AN ORANGE.

2. Originally Posted by Zandra
a basket has 3 oranges 4 apples & 3 MANGOES. IN HOW MANY WAYS 2 FRUITS CAN BE CHOSEN FROM THE BASKET ? HOW MANY OF THEM WILL CONTAIN AN ORANGE.
I assume the fruits don't have to be different (you don't say one way or the other so I assume so).

Originally Posted by Zandra
a basket has 3 oranges 4 apples & 3 MANGOES. IN HOW MANY WAYS 2 FRUITS CAN BE CHOSEN FROM THE BASKET ?[snip]
There are 10 fruit altogether and you want to choose 2: $\displaystyle ^{10}C_2$.

Originally Posted by Zandra
[snip]IN HOW MANY WAYS 2 FRUITS CAN BE CHOSEN FROM THE BASKET ? HOW MANY OF THEM WILL CONTAIN AN ORANGE.
Two methods:

1. If there's no oranges then you are choosing 2 fruit from 7: $\displaystyle ^{7}C_2$. So the number of combinations with oranges will be $\displaystyle ^{10}C_2 - ^{7}C_2$.

2. (Choose 1 orange from 3 and 1 non-orange from 7) + (Choose 2 oranges from 3 and 0 non-orange from 7): $\displaystyle ^{3}C_1 \times ^{7}C_1 + ^{3}C_2 \times ^{7}C_0$.

Both methods obviously give the same answer.