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    A box of 20 biscuits contains 4 different chocolate biscuits, 2 different oatmeal biscuits and 14 different ginger biscuits. 6 biscuits are selected from the box at random.
    (i) Find the number of different selections that include the 2 oatmeal biscuits.

    So I've tried using :
    Excluding oatmeal = 18C2, No restrictions = 20C6
    Selections = 20C6 - 18C2
    =20196

    But the correct answer is 18C4 = 3060

    I understand the answer's method, but could someone explain why my initial method is incorrect? Thanks
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    (Original post by sourmango1)
    A box of 20 biscuits contains 4 different chocolate biscuits, 2 different oatmeal biscuits and 14 different ginger biscuits. 6 biscuits are selected from the box at random.
    (i) Find the number of different selections that include the 2 oatmeal biscuits.

    So I've tried using :
    Excluding oatmeal = 18C2, No restrictions = 20C6
    Selections = 20C6 - 18C2
    =20196

    But the correct answer is 18C4 = 3060

    I understand the answer's method, but could someone explain why my initial method is incorrect? Thanks
    For your approach to work, you would have to calculate it as unrestricted combinations - combinations with neither of the oatmeals - combinations with exactly one of the oatmeals. This would leave you with the combinations with two oatmeals as required. You have omitted the third element.

    (Also I'm guessing you mean 18C6 where you've written 18C2).
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    (Original post by old_engineer)
    For your approach to work, you would have to calculate it as unrestricted combinations - combinations with neither of the oatmeals - combinations with exactly one of the oatmeals. This would leave you with the combinations with two oatmeals as required. You have omitted the third element.

    (Also I'm guessing you mean 18C6 where you've written 18C2).
    Ah yes I meant 18C6. Thank you I understand now.
 
 
 
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