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Bunuel
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?

(A) 6
(B) 12
(C) 24
(D) 36
(E) 48

We need a 7 digit number with two 2s, two 3s and three 5s. Whatever comes in first 3 spots needs to come in the last 3 spots too so it will be in pairs. The only extra digit is a 5. Hence we will have

__ __ __ 5 __ __ __

Now, 2,3 and 5 can be arranged in the first 3 spots in 3! ways = 6 ways. Whatever the arrangement, the same arrangement will need to be maintained in the last 3 spots in reverse order e.g. 2 3 5 5 5 3 2

Hence there are only 6 ways of writing a palindrome.
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