How many $7$ digit palindromes can be formed using the digits $2,2,3,3,5,5,5?$
+321 We can write this number as abcdcba. We know that d must be 5 since there are an odd number of fives. We now have 3 choices left for a,b, and c. Each of the permutations of those 3 choices will end up in 6 different palindromes that can be formed.
