# Bankteller Problem: How Many Ways Can Both Men and Women Be Served?

• rickdundee
In summary, the problem involves 6 males and 4 females waiting to see a teller at a bank, with only 4 people being able to be served at one time. The first question asks how many ways 4 people can be picked and served, including 2 men and 2 women. The second question asks for the probability of 4 randomly picked people including 2 men and 2 women. The solutions for these questions are (6 choose 2) * (4 choose 2) = 90 and 6C3 x 4C2 / 10C4 = 3/7, respectively. Another similar problem involves 5 tellers serving 5 people at once, with the requirement of

#### rickdundee

HELP! Bankteller Problem

1. Homework Statement
There are 6 males and 4 females awaiting to see a teller at a bank.

Only 4 people can be served at one time.
1) How many ways can four of the people be picked and served one at a time, if they must include two(2) men and two(2) women?

2) If indeed the four people are picked randomly, what is the probability that the four will include two (2) men and two (2) women?
This is the question I am confused about.

3. The Attempt at a Solution
My solution for Problem#1: (6 choose 2) * (4 choose 2) = 90

2) 6C2 x 4C2 /10C4 = 3/7

Last edited:
HELP! Bankteller Problem

Thank you. Could you check this.

It is the end of the day and there are 5 tellers, but each teller can only serve one person. Therefore only five people can be served, each by a teller, so the five people are picked at once.

1) How many ways can five of the people picked and served, if they must include 3 men and 2 women?

My solution: (10c5)*(6c3)*(4c2)

2) If indeed the 5 people are picked randomly, what is the probability that the five will include 3 men and 2 women?

My solution: If the solution to the first question is correct I should be able to figure it out.

This is bound to be homework.

Actually review of an even answer in the text.

2) Just as before,
6C3 x 4C2 / 10C5 =10/21

## 1. What is the "HELP Bankteller Problem"?

The "HELP Bankteller Problem" is a mathematical riddle that involves a bankteller who has trouble counting cash and an impatient customer.

## 2. How does the "HELP Bankteller Problem" go?

The riddle goes like this: A bankteller gives a customer $100 in cash. The customer counts the money and realizes that the bankteller has made a mistake and given him$10 too much. The customer returns the $10 to the bankteller, who thanks him and continues with his work. However, after the customer leaves, the bankteller realizes that he made a mistake and gave the customer$10 too little. The bankteller is left with a dilemma - should he correct his mistake and give the customer the missing $10, or keep the$10 for himself?

## 3. What is the solution to the "HELP Bankteller Problem"?

The answer to the "HELP Bankteller Problem" is that the bankteller should return the $10 to the customer. This is because the bankteller's initial mistake of giving the customer$10 too little was unintentional, while his second mistake of keeping the \$10 would be a deliberate act of dishonesty.

## 4. What is the significance of the "HELP Bankteller Problem"?

The riddle highlights the ethical dilemma that individuals may face in certain situations, where they have to choose between doing what is right and what is convenient. It also emphasizes the importance of honesty and integrity in professional settings, particularly in the banking industry where trust is crucial.

## 5. Is the "HELP Bankteller Problem" a real-life scenario?

The "HELP Bankteller Problem" is a fictional scenario created to illustrate a moral dilemma. However, similar situations may arise in real life and it is important for individuals to make ethical decisions in such situations.