In how many ways can 5 sets of numbers be picked from 50 numbers in a lottery?
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.
![**Combinations:**
In permutations, order mattered even though repetition was not allowed. In combinations, order does NOT matter and repetition is still not allowed.
**Example and Exercise:**
The math department with 15 professors has to send 3 delegates to a convention. In how many ways can these delegates be selected?
Start: \(15 * 14 * 13\),
then internally rearrange the committee of three since order and titles don’t matter.
Solution:
\[
\frac{{15 * 14 * 13}}{{3 * 2 * 1}} = 455
\]
**Question:**
In how many ways can 5 sets of numbers be picked from 50 numbers in a lottery?
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