Permutations and Combinations of Numbers from 1 to 36

When dealing with combinations and permutations, it's essential to understand the underlying principles and formulas to accurately calculate the possibilities. In this article, we will explore the number of combinations of 4 through 1 to 36 and the variety of combinations one can form using these numbers. Let's dive into the details and discover the mathematical magic behind it all.

Combinations of 4 Numbers

Assuming the set of numbers is the integers from 1 to 36, we can calculate the number of combinations using the formula:

nCr n! / (n-r)!r!, where n is the number of items to choose from, and r is the number of items chosen at a time.

For our case:

36C4 36! / (36-4)!4!

Calculating the factorial, we get:

36C4 36! / 32!4!

Simplifying further:

36C4 3635343332 / 24

36C4 58905

Note that it's easy to write a program to generate all 58,905 4-number combinations, and the first combination is [1 2 3 4], while the last is [33 34 35 36]. This illustrates the vast number of unique combinations possible from a set of 36 numbers.