Question

An urn contains 7 white balls and 3 red balls. Three balls are selected. In how many ways can the 3 balls be drawn from the total of 10 balls: (a) If 2 balls are white and 1 is red? (b) If all 3 balls are white? (c) If all 3 balls are red?

Name: Problem 53, Chapter 12: Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry
Uploaded: 2021-06-26T19:47:55-08:00
Duration: 2 min 6 s
Channel: Sheryl Ezze
Description: An urn contains 7 white balls and 3 red balls. Three balls are selected. In how many ways can the 3 balls be drawn from the total of 10 balls: (a) If 2 balls are white and 1 is red? (b) If all 3 balls are white? (c) If all 3 balls are red?

   An urn contains 7 white balls and 3 red balls. Three balls are selected. In how many ways can the 3 balls be drawn from the total of 10 balls:
(a) If 2 balls are white and 1 is red?
(b) If all 3 balls are white?
(c) If all 3 balls are red?

Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry

Michael Sullivan,… 3rd Edition

Chapter 12, Problem 53

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Solved by Expert Sheryl Ezze

06/26/2021

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An urn contains 7 white balls and 3 red balls. Three balls are selected. In how many ways can the 3 balls be drawn from the total of 10 balls: (a) If 2 balls are white and 1 is red? (b) If all 3 balls are white? (c) If all 3 balls are red?

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Key Concepts

Combinations

The concept of combinations involves selecting items from a larger set where the order of selection does not matter. It is typically represented by the binomial coefficient, often written as C(n, k) or n choose k, which calculates the number of ways to choose k elements from a set of n elements.

Counting with Conditions

Counting with conditions means breaking down a problem into cases based on specified requirements and using combinatorial methods to calculate the number of outcomes for each case. This approach is essential when selections must satisfy specific criteria, such as having a certain number of items from different subgroups.

Binomial Coefficients

Binomial coefficients are fundamental in combinatorial calculations and represent the number of ways to choose a subset from a larger set. They form the basis of applying the combinations formula in various selection problems, particularly when dealing with selections from distinct groups.

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