<p>How many <img alt="$7$" height="12" src="https://latex.artofproblemsolving.com/e/0/a/e0a0db32027a732ac57d37ef2ae9bb150f65b108.png" width="9" />-digit palindromes (numbers that read the same backward as forward) can be formed using the digits <img alt="$2$" height="12" src="https://latex.artofproblemsolving.com/4/1/c/41c544263a265ff15498ee45f7392c5f86c6d151.png" width="8" />, <img alt="$2$" height="12" src="https://latex.artofproblemsolving.com/4/1/c/41c544263a265ff15498ee45f7392c5f86c6d151.png" width="8" />, <img alt="$3$" height="12" src="https://latex.artofproblemsolving.com/7/c/d/7cde695f2e4542fd01f860a89189f47a27143b66.png" width="8" />, <img alt="$3$" height="12" src="https://latex.artofproblemsolving.com/7/c/d/7cde695f2e4542fd01f860a89189f47a27143b66.png" width="8" />, <img alt="$5$" height="12" src="https://latex.artofproblemsolving.com/7/9/0/79069377f91364c2f87a64e5f9f562a091c8a6c1.png" width="8" />, <img alt="$5$" height="12" src="https://latex.artofproblemsolving.com/7/9/0/79069377f91364c2f87a64e5f9f562a091c8a6c1.png" width="8" />, <img alt="$5$" height="12" src="https://latex.artofproblemsolving.com/7/9/0/79069377f91364c2f87a64e5f9f562a091c8a6c1.png" width="8" />?</p>

Question No: 287

How many $7$ -digit palindromes (numbers that read the same backward as forward) can be formed using the digits $2$ , $2$ , $3$ , $3$ , $5$ , $5$ , $5$ ?

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Tags: Algebra Probability

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