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Math Help - balls problems

  1. #1
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    balls problems


    1. A BOX CONTAINS 4RED,3BLUE AND 2WHITES BALLS,IN HOW MANY WAYS CAN WE SELECT 3BALLS SUCH THAT:

    A. THEY ARE ALL DIFFERENT COLOR
    B. THEY ARE ALL RED
    C. 2 ARE BLUE 1 IS WHITE
    D. EXACTLY 2 ARE BLUE
    E. NONE IS WHITE
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  2. #2
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    Hello, hany!

    Take off your CAPS LOCK.
    It's hard to read . . . and it's impolite to
    SHOUT.

    A box contains 4 red, 3 blue and 2 white balls.
    In how many ways can we select 3 balls such that:
    A) They are all different colors.

    \underbrace{(_4C_1)}_{\text{1 R}}\underbrace{(_3C_1)}_{\text{1 B}}\underbrace{(_2C_1)}_{\text{1 W}} \:=\:4\cdot3\cdot2 \:=\:24\text{ ways.}



    B) They are all red.

    \underbrace{_4C_3}_{\text{3 R}} \;=\;4\text{ ways.}



    C) Two are blue, one is white.


    \underbrace{(_3C_2)}_{\text{2 B}}\underbrace{(_2C_1)}_{\text{1 W}} \:=\:6\text{ ways.}



    D) Exactly two are blue.
    There are 3 Blues and 6 Others.

    \underbrace{(_3C_2)}_{\text{2 B}}\underbrace{(_6C_1)}_{\text{1 Other}} \:=\:18\text{ ways.}



    E) None is white.
    There are 7 non-white balls.

    \underbrace{_7C_3}_{\text{3 not-W}} \:=\:35\text{ ways.}

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