Question

A committee of six people is to be chosen from a group of 15 people that contains two married couples. a) What is the probability that the committee will include both married couples? b) What is the probability that the committee will include the three youngest members in the group?

Name: Problem 18, Chapter 12: Higher Level Mathematics
Uploaded: 2020-05-13T17:22:07-08:00
Duration: 1 min 20 s
Channel: Julian Wong
Description: A committee of six people is to be chosen from a group of 15 people that contains two married couples. a) What is the probability that the committee will include both married couples? b) What is the probability that the committee will include the three youngest members in the group?

   A committee of six people is to be chosen from a group of 15 people that contains two married couples.
a) What is the probability that the committee will include both married couples?
b) What is the probability that the committee will include the three youngest members in the group?

Higher Level Mathematics

Ibrahim Wazir, Tim… 2012 Edition

Chapter 12, Problem 18

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Solved by Expert Julian Wong

05/13/2020

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A committee of six people is to be chosen from a group of 15 people that contains two married couples. a) What is the probability that the committee will include both married couples? b) What is the probability that the committee will include the three youngest members in the group?

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Key Concepts

Combinations

This concept involves choosing a subset of items from a larger set where the order of selection does not matter, typically calculated using the binomial coefficient ('n choose k'). It is a foundational tool in probability and counting problems, such as determining the total number of possible committees.

Combinatorial Probability

This concept refers to calculating the probability of an event by taking the ratio of the number of favorable outcomes to the total number of possible outcomes. It is particularly useful in problems that involve random selections or committees from a given set of elements.

Restricted Selection

This concept deals with counting outcomes under additional constraints, such as requiring specific individuals to be included in the selection. By fixing some selections (like mandatory members), the total number of choices is reduced, and the count of favorable outcomes is adjusted accordingly.

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