Assume the following pattern with terms built of square tile figures continues and complete parts (a) through (c) below. a. How many square tiles are there in the ninth figure? b. How many square tiles are in the nth figure? O A. The figures do not appear to follow any predictable pattern. O B. There are 3n -1 square tiles in the nth figure. OC. There are 3n + 1 square tiles in the nth figure. O D. There are 3n square tiles in the nth figure. c. Is there a figure that has exactly 509 square tiles? If so, which one? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. Yes. Figure number has 509 square tiles. O B. No. There does not exist a figure with exactly 509 square tiles.

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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.