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Math Help - probability

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    Smile 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.
    Last edited by Zandra; December 16th 2008 at 09:42 PM.
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  2. #2
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    Quote Originally Posted by Zandra View Post
    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).

    Quote Originally Posted by Zandra View Post
    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: ^{10}C_2.

    Quote Originally Posted by Zandra View Post
    [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: ^{7}C_2. So the number of combinations with oranges will be ^{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):  ^{3}C_1 \times ^{7}C_1 + ^{3}C_2 \times ^{7}C_0.

    Both methods obviously give the same answer.
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