SOLUTION: A committee of 4 people is to be formed from a pool of 8 people. What is the probability James is in the committee?

Question 1197366: A committee of 4 people is to be formed from a pool of 8 people. What is the probability James is in the
committee?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52777)   (Show Source): You can put this solution on YOUR website!
.

P = = = = 0.5 = 50%. ANSWER

The denominator is the number of all different possible quadruples of 8.

The numerator is the number of all such quadruples containing James.

Solved and explained.

-----------------

This problem assumes that you are familiar with COMBINATIONS - - - this knowledge is a pre-requisite.

On Combinations, see introductory lessons
    - Introduction to Combinations
    - PROOF of the formula on the number of Combinations
    - Problems on Combinations
in this site.

Also, you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Combinatorics: Combinations and permutations".

Save the link to this textbook together with its description

Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson

into your archive and use when it is needed.

\\\\\\\\\\\\\\\\\\\

Sometimes, when I explain such solutions to students, I calculate the number of combinations manually,
using and showing explicit formulas.

But had I do it this way every time, I, probably, would lose my mind.

Therefore, often I use MS Excel software in my computer writing

            =combin(N,n), when I need the value   .

Answer by greenestamps(13198)   (Show Source): You can put this solution on YOUR website!

You should understand the solution shown by tutor @ikleyn.

However, for this particular type of probability problem, there is a much simpler path to the answer.

4 of the 8 people are to be on the committee; the probability that James (or any particular one of them) is on the committee is 4/8 = 1/2.

You can see how this result is obtained by looking at the details of the calculation shown by the other tutor:

RELATED QUESTIONS
A committee of 4 people is to be selected from a group consisting of 8 men and 4 women. (answered by Edwin McCravy)
A committee of 4 people is randomly selected from a group of 5 Republicans and 6... (answered by ewatrrr)
How many ways can a 4 person committee be formed from a group of 8 people, if Jon must be (answered by stanbon)
A committee of 5 people is to be formed from 10 doctors and 8 dentists. Find the... (answered by stanbon)
A committee of 4 people is to be chosen from a group of 19 people. One person is the... (answered by sudhanshu_kmr)
To make a committee 4 men are to be chosen out of 6 candidates. What is the probability... (answered by greenestamps)
From a group of 7 men and 5 women, a committee of 5 people is to be chosen. If each... (answered by ewatrrr)
A school committee consists of four people. The committee can be formed from 20 teachers... (answered by Solver92311)
. A committee of 4 people is to be selected from a group of 5 men and 7 women. If the... (answered by ikleyn)