2009 AMC 10B Problems/Problem 11

Problem

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

$\text{(A) } 6 \qquad \text{(B) } 12 \qquad \text{(C) } 24 \qquad \text{(D) } 36 \qquad \text{(E) } 48$

Solution

A seven-digit palindrome is a number of the form $\overline{abcdcba}$ . Clearly, $d$ must be $5$ , as we have an odd number of fives. We are then left with $\{a,b,c\} = \{2,3,5\}$ . Each of the $\boxed{6}$ permutations of the set $\{2,3,5\}$ will give us one palindrome.

2009 AMC 10B (Problems • Answer Key • Resources)
Preceded by Problem 10	Followed by Problem 12
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2009 AMC 10B Problems/Problem 11

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