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Help me solve this Combination maths problem

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    This is an IGCSE additional mathematics permutation combination problem which I can't understand. Can somebody explain how this is done? My teacher says the question is incomplete.

    Question
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    A box contains sweets of 6 different flavours. There are at least 2 sweets of each flavour. A girl selects 3 sweets from the box. Given that these 3 sweets are not all of the same flavour, calculate the number of different ways she can select her 3 sweets.

    Answer
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    3 Different = 6C2 = 20
    2 of 1 kind + 1 = 6 * 5 = 30

    Total = 2- + 30 = 50
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    (Original post by Paing Thet)
    This is an IGCSE additional mathematics permutation combination problem which I can't understand. Can somebody explain how this is done? My teacher says the question is incomplete.

    Question
    ---------------------------------------------------------
    A box contains sweets of 6 different flavours. There are at least 2 sweets of each flavour. A girl selects 3 sweets from the box. Given that these 3 sweets are not all of the same flavour, calculate the number of different ways she can select her 3 sweets.

    Answer
    --------------------------------------------------------
    3 Different = 6C2 = 20
    2 of 1 kind + 1 = 6 * 5 = 30

    Total = 2- + 30 = 50
    The question is complete, but there is a typo in the answer you've put.

    Since the three chosen sweets are not all of the same flavour, either she has chosen 3 different flavours, or she has chosen 2 different flavours.

    If 3 different, then she is choosing 3 from 6, and we have 6C3 = 20.

    If there are two different flavours, then there is one of one flavour and two of a different flavour.
    The one has 6 choices of flavours and once chosen the two have five choices, making 6x5=30 possibilities.

    Hence 50 ways in total.
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    (Original post by ghostwalker)
    The question is complete, but there is a typo in the answer you've put.

    Since the three chosen sweets are not all of the same flavour, either she has chosen 3 different flavours, or she has chosen 2 different flavours.

    If 3 different, then she is choosing 3 from 6, and we have 6C3 = 20.

    If there are two different flavours, then there is one of one flavour and two of a different flavour.
    The one has 6 choices of flavours and once chosen the two have five choices, making 6x5=30 possibilities.

    Hence 50 ways in total.
    Wow, I understand it now. Thanks
 
 
 
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