Question

Use the formula for $_{n} C_{r}$ to solve Exercises $49-56$ 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?

Name: Problem 55, Chapter 10: Precalculus
Uploaded: 2021-08-20T22:15:14-08:00
Duration: 1 min 3 s
Channel: Madysn Cardinal
Description: Use the formula for n Cr to solve Exercises 49-56 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?

   Use the formula for $_{n} C_{r}$ to solve Exercises $49-56$
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?

Precalculus

Robert Blitzer 6th Edition

Chapter 10, Problem 55

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Solved by Expert Madysn Cardinal

08/20/2021

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This is a combination problem, since the order in which the numbers are selected does not matter. Show more…

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Use the formula for $_{n} C_{r}$ to solve Exercises $49-56$ 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?

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Key Concepts

Combinations

This concept involves selecting a subset of items from a larger set where the order of selection does not matter. It is commonly used in probability and counting problems to determine the number of ways to choose 'r' items from 'n' available items without regard to sequence.

Combination Formula (nCr)

This is a mathematical formula used to calculate the number of combinations possible when selecting a subset of items from a larger set. It is given by the formula nCr = n! / (r!(n - r)!), where 'n' is the total number of items, 'r' is the number of items being chosen, and '!' denotes factorial.

Factorial

Factorial is a function that multiplies a number by every positive integer less than itself. It is denoted by an exclamation mark (n!), and is essential in calculating combinations and permutations as it represents the product of a series of descending natural numbers.

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