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Chapter 11: Problem 55

To win at LOTTO in the state of Florida, one must correctly select 6 numbers from a collection of 53 numbers (1 through 53). The order in which the selection is made does not matter. How many different selections are possible?

Short Answer

Expert verified
The total number of ways 6 numbers can be selected from 53 is calculated to be 22,957,480.

Step by step solution

01

Understanding Combinations

In mathematics, a combination is a selection of items without regard to the order of selection. So, we need to find the number of combinations of picking 6 numbers out of 53. The formula for combinations is \(C(n, r) = \frac{n!}{r!(n-r)!}\) where \(n\) is the total number of items, \(r\) is the number of items to choose, and \( ! \) denotes factorial.
02

Identify Variables in the Problem

In this problem, \(n = 53\) because there are 53 total numbers to choose from, and \(r = 6\) because we are choosing 6 numbers. Now we just need to plug these values into the combination formula.
03

Apply Method and Calculate

Substitute the values of \(n\) and \(r\) in the combination formula, we get \(C(53, 6) = \frac{53!}{6!(53-6)!}\). Calculate the factorials and simplifying, we can get the total number of ways 6 numbers can be selected from 53.

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