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Ra Ghazi
Ra Ghazi asked in Science & MathematicsMathematics · 8 years ago

Help understanding combinatorics?

How many ways are there to form a list of three letters from the letters in the word COMBINATORICS if the letters cannot be used more often than they appear in COMBINATORICS?

Can someone please explain this to me?

Update:

Order doesnt matter

1 Answer

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  • Guy
    Lv 7
    8 years ago
    Favorite Answer

    Here are the letters and their corresponding frequencies:

    1 A

    1 B

    2 C’s

    2 I’s

    1 M

    1 N

    2 O’s

    1 R

    1 S

    1 T

    First let’s deal with combinations that have no repeating letters. There are 10 distinct letters and we are choosing 3 at a time. 10C3 = 120.

    Now let’s count the number of combinations that have 1 repeating letter.

    There are 9 combinations of 2 C’s with one other letter.

    There are 9 combinations of 2 I’s with one other letter.

    There are 9 combinations of 2 O’s with one other letter.

    This means there are 9(3) = 27 arrangements that contain two letters.

    Total = 120 (plus) 27 = 147

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