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Chapter 11: Problem 69

What is a combination?

Short Answer

Expert verified
A combination is a mathematical concept used to find the number of ways a certain number of items can be selected from a larger set, without considering the order of selection.

Step by step solution

01

Defining Combination

A combination is a selection of items from a larger set where the order of selection does not matter. In mathematics, combinations are used in probability and statistics, among other fields. Combination is often symbolized as \( C(n, r) \) or \(_nC_r \) , where 'n' is the total number of items and 'r' is the number of items to select.
02

Example of Combination

For instance, if you are given a deck of 52 playing cards, and you are asked how many different 5-card hands you can make, you would use combinations to solve the problem. The notation of the combination would be denoted as \( C(52, 5) \).
03

Computing Combination

Combinations can be calculated using the formula \( C(n, r) = n! / [r!(n-r)!] \), where 'n!' denotes n-factorial, the product of all positive integers up to n. For the example provided, it would be \( C(52, 5) = 52! / [5!(52-5)!] \).

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