Explain in your own words why we compare num- bers in the decimal system by starting at the left- most place at which there is a nonzero digit and then proceeding to the right if necessary. For exam- ple, we compare 234 and 219 by starting at the hun- dreds place and then moving to the tens place. We compare 1122 and 987 by starting at the thousands place. What is it about the decimal system that al- lows us to compare numbers this way?
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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