A bag contains one green marble, one red marble, and one...

Name: Problem 52, Chapter 12: Geometry A Common Core Curriculum
Uploaded: 2021-01-02T20:08:27-08:00
Duration: 2 min 58 s
Channel: Timothy Behan
Description: A bag contains one green marble, one red marble, and one blue marble. The diagram shows the possible outcomes of randomly drawing three marbles from the bag without replacement. a. How many combinations of three marbles can be drawn from the bag? Explain. b. How many permutations of three marbles can be drawn from the bag? Explain.

A bag contains one green marble, one red marble, and one blue marble. The diagram shows the possible outcomes of randomly drawing three marbles from the bag without replacement. a. How many combinations of three marbles can be drawn from the bag? Explain. b. How many permutations of three marbles can be drawn from the bag? Explain.

A bag contains one green marble, one red marble, and one blue marble. The diagram shows the possible outcomes of randomly drawing three marbles from the bag without replacement.
a. How many combinations of three marbles can be drawn from the bag? Explain.
b. How many permutations of three marbles can be drawn from the bag? Explain.

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Key Concepts

Combinations

Combinations are a fundamental concept in combinatorics where the selection of items is done without regard to the order. This means that when choosing items, different orders of the same group result in the same combination. The formula for combinations is nCr = n! / (r!(n - r)!), where n is the total number of items and r is the number of items to choose.

Permutations

Permutations are another key concept in combinatorics that deal with the arrangement or ordering of items. Unlike combinations, the order in which the items are arranged matters in permutations. The formula used is nPr = n! / (n - r)!, where n is the total number of items and r is the number of items to arrange.

Factorial

The factorial, denoted by n!, is a mathematical operation that multiplies a positive integer n by all positive integers less than itself. Factorials are used in both combination and permutation calculations to account for the number of ways to order or select items, and they are a fundamental part of these formulas.

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