Problem 55 - Algebra and Trigonometry

Question

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?

Step-by-Step Solution

Answer

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

Step 1: 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.

Step 2: 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.

Step 3: 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.