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Math Help - Check Combinations

  1. #1
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    Check Combinations

    A large pile of coins consists of pennies, nickels, dimes and quarters.

    a) How many different collections of 30 coins can be chosen if there are at least 30 of each kind of coin?
    b) If the pile contains only 15 quarters but at least 30 of each other kind of coin, how many collections of 30 coins can be chosen?

    Is the answer to part (a) C(30,4)? What about part (b)?
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  2. #2
    Senior Member abhishekkgp's Avatar
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    Re: Check Combinations

    Quote Originally Posted by lovesmath View Post
    A large pile of coins consists of pennies, nickels, dimes and quarters.

    a) How many different collections of 30 coins can be chosen if there are at least 30 of each kind of coin?
    b) If the pile contains only 15 quarters but at least 30 of each other kind of coin, how many collections of 30 coins can be chosen?

    Is the answer to part (a) C(30,4)? What about part (b)?
    answer to part a) is not C(30,4). it is C(33,3). it is equivalent to finding the number of non-negative integral solutions of x+y+z+w=30.
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  3. #3
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    Re: Check Combinations

    Is part (b) C(18,3) + C(33,3)?
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  4. #4
    Senior Member abhishekkgp's Avatar
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    Re: Check Combinations

    Quote Originally Posted by lovesmath View Post
    Is part (b) C(18,3) + C(33,3)?
    the answer to part b) should obviously be less than the answer to part a).
    my answer for part b) is C(33,3)-C(17,3)
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