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A palindrome is a number that reads the same forward and backward. For example. 2442 and 111 are palindromes. If 5-digit palindromes are formed using one or more of the digits, 1, 2, 3, how many such palindromes are possible?
A) 12
B) 15
C) 18
D) 24
E) 27
To read the same forward and backward, the 5-digit integer must look as follows:
ABCBA.
The ten-thousands digit and the units digit must be THE SAME.
The thousands digit and the tens digit must also be THE SAME.
Number of options for the ten-thousands digit = 3. (1, 2, or 3)
Number of options for the units digit = 1. (Must be the same as the ten-thousands digit)
Number of options for the thousands digit = 3. (1, 2, or 3)
Number of options for the tens digit = 1. (Must be the same as the thousands digit)
Number of options for the hundreds digit = 3. (1, 2, or 3)
To combine these options, we multiply:
3*3*3*1*1 = 27.
The correct answer is
E.
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