. I selected 10 letters fromp a bag of letter tiles. In this case, all ten of the letters are distinct. In how many different orders can these letters be arranged? b. How many different orderings are there for any 6 of these 10 letters? c. Suppose that instead of ten distinct letters, I selected a few repeats. Assume the collection of letters (with) repeats, ismthe following: A, A, A, B, C, C, E, E, T, T How many different arrangements can be made with this group of letters?
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.
a. I selected 10 letters fromp a bag of letter tiles. In this case, all ten of the letters are distinct.
In how many different orders can these letters be arranged?
b. How many different orderings are there for any 6 of these 10 letters?
c. Suppose that instead of ten distinct letters, I selected a few repeats.
Assume the collection of letters (with) repeats, ismthe following:
A, A, A, B, C, C, E, E, T, T
How many different arrangements can be made with this group of letters?
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