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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.
Combinatorial questions:
a. In how many ways a strings with 6 characters can be ordered assuming all characters are different?
b. If a bit could store 4 numbers instead of 2, how many numbers a byte could hold?
c. How many 4 character different “words” you can make out of permutations of string “abcdefg”?
d. How many different sets of cardinality 3 can you make out of string “abcdefg”?
e. In how many distinct ways a strings “aaaabbbcc” can be ordered?
f. In how many different ways you can distribute 9 same candies between 3 children?
g. In how many different ways you can distribute 9 different candies between 3 children if you have 4 chocolates, 3 gummy bears, and 2 caramels?
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