How many palindromes can be made...? Please help!?

using all of the letters contained in the phrase 'NEVER ODD OR EVEN'?

Help! How do I solve this! (Grade 12 Data Management, Counting Principles and Permutations).

I know that you split the 'word' in half, leaving how ever many options you have on the right, mirrored on the left. And since there's repetition in the word with the double E's I have to account for this as well correct?

is it something like this? 7 x 6 x 5 x 4 x 3 x 2 x 1 | 1 x 1 x 1 x 1 x 1 x 1

but in the actual equation, 7! / 2! (the 2! being the double E's?)

I don't know, please help!

Update:

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1 Answer

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  • Todd
    Lv 6
    9 years ago
    Favorite Answer

    We need a count of each letter:

    N: 2

    E: 4

    V: 2

    R: 2

    O: 2

    D: 2

    Thus, each side will have one of each letter except for E which will be twice.

    If each letter were unique, we would have 7!. But because two of the letters are the same, we divide by the number combinations of those common letters, which is 2!.

    Thus, solution is 7! / 2!.

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