💯 Unordered Selections by Combinations, An Ultimate Guide. Watch this video!

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Timeline:
0:00 Intro
0:48 Question 7 Choosing 4 books from 7
1:36 Question 8 Forming a Committee
5:23 Question 9 A Family with at least one Adult
7:43 Question 10 Forming Words with Repetitions

Unordered selections, also known as combinations, refer to the number of ways to choose k items from a set of n items without regard to order.

For example, suppose you have a set of 5 items, A, B, C, D, and E, and you want to choose 2 items. The combinations would be: AB, AC, AD, AE, BC, BD, BE, CD, and CE. The total number of combinations would be C(5,2) = 10, where C(n, k) represents the number of combinations of n items taken k at a time.

The formula for calculating combinations is C(n, k) = n! / (k! (n-k)!). Here, n! represents n factorial, which is the product of all positive integers up to n (e.g. 5! = 5 x 4 x 3 x 2 x 1 = 120). The term k! represents k factorial, and (n-k)! represents (n-k) factorial.

Combinations are important in various fields, including probability and statistics, where they are used to calculate the number of possible outcomes for an event, as well as in computer science and cryptography, where they are used in combination algorithms.