10. Play the Tower of Hanoi and determine the minimum number of moves required to transfer the disks from the peg to the third peg for each of the following situations. a. You start with only one disk. b. You start with two disks. c. You start with three disks. (Note: You can use a stack of various size coins to simulate the puzzle, or you can use one of the many websites that provide a simulation of the puzzle. Ex. https://www.mathisfun.con/games/towerofhanoi.html) d. You start with four disks. e. You start with fi ve disks. I. You start with n disks.
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.
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