Question

A student committee has 6 members-4 undergraduate and 2 graduate students. A subcommittee of 3 members is to be chosen randomly so that each possible combination of 3 of the 6 students is equally likely to be selected. What is the probability that there will be no graduate students on the subcommittee?

Name: Problem 31, Chapter 3: Statistics for Business and Economics
Uploaded: 2021-12-26T14:04:34-08:00
Duration: 1 min 13 s
Channel: Christopher Stanley
Description: A student committee has 6 members-4 undergraduate and 2 graduate students. A subcommittee of 3 members is to be chosen randomly so that each possible combination of 3 of the 6 students is equally likely to be selected. What is the probability that there will be no graduate students on the subcommittee?

   A student committee has 6 members-4 undergraduate and 2 graduate students. A subcommittee of 3 members is to be chosen randomly so that each possible combination of 3 of the 6 students is equally likely to be selected. What is the probability that there will be no graduate students on the subcommittee?

Statistics for Business and Economics

Paul Newbold,… 8th Edition

Chapter 3, Problem 31

Instant Answer

Solved by Expert Christopher Stanley

12/26/2021

Step 1

This can be calculated using the combination formula, which is denoted as ${n \choose k}$, where $n$ is the total number of items, and $k$ is the number of items to choose. So, the total number of ways to choose a subcommittee of 3 members from a committee of 6 Show more…

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A student committee has 6 members-4 undergraduate and 2 graduate students. A subcommittee of 3 members is to be chosen randomly so that each possible combination of 3 of the 6 students is equally likely to be selected. What is the probability that there will be no graduate students on the subcommittee?

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Key Concepts

Combinatorics

Combinatorics is a branch of mathematics concerned with counting, arranging, and analyzing configurations of objects. In the context of selection and committee problems, it provides methods for determining how many ways items can be chosen, which is essential for calculating probabilities.

Binomial Coefficients

Binomial coefficients, commonly notated as 'n choose k', are used to calculate the number of ways to select a subset of elements from a larger set without regard to order. This concept is crucial for determining both the total number of possible groups and the number of favorable groups in problems involving random selection.

Probability Calculation

Probability calculation involves finding the ratio of the number of favorable outcomes to the total number of outcomes. In problems where selections are made at random, using combinatorial methods to count these outcomes is key to determining the likelihood of specific conditions being met.

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