A palindrome is a number that reads the same forward and backward, such as 2,743,472. (a) Give a clear but brief argument showing that every palindrome with an even number of digits is divisible by 11. (b) Is it possible for a palindrome with an odd number of digits to be divisible by 11? Explain. (a) Choose the correct answer below. O A. The sum of the digits will always be a non-zero multiple of 11 and therefore a palindrome with an even number of digits will always be divisible by 11. O B. The sum of the digits will always be 0 and therefore a palindrome with an even number of digits will always be divisible by 11.

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Permutations and Combinations

If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.

Counting Theory

The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.