Permutations & Combinations: Bankteller Problem

In summary, there are 6 males and 4 females waiting to be served by a teller at a bank. Only 4 people can be served at a time. To determine the number of ways to pick and serve four people, if two of them must be men and two of them must be women, you would use the formula (6 choose 2) * (4 choose 2) = 90. For the second question, the probability of picking four people randomly and having two men and two women is 90/210 = 3/7.
  • #1
rickdundee
10
0

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.


The Attempt at a Solution


My solution for Problem#1: (6 choose 2) * (4 choose 2) = 90
 
Physics news on Phys.org
  • #2
How many ways can you pick 4 people out of the 4 men and 6 women (with no restriction on how many men or women there are)?
 
  • #3
That would be 10c4
 

1. What is the difference between permutations and combinations?

Permutations refer to the arrangement of a set of objects in a specific order, while combinations refer to the selection of objects from a set without considering the order.

2. How is the bankteller problem related to permutations and combinations?

The bankteller problem involves calculating the number of ways a certain number of customers can be served by a certain number of banktellers, which is an example of a combinations problem.

3. How do you calculate the number of combinations in the bankteller problem?

The number of combinations in the bankteller problem can be calculated using the formula nCr = n! / (r! * (n-r)!), where n is the total number of customers and r is the number of banktellers.

4. What is the difference between a permutation and a combination in the context of the bankteller problem?

A permutation in the bankteller problem would involve calculating the number of ways the customers can be served in a specific order, while a combination only considers the selection of customers without any specific order.

5. Can the bankteller problem be solved using both permutations and combinations?

Yes, the bankteller problem can be solved using both permutations and combinations depending on the specific question being asked. For example, if the question asks for the number of ways the customers can be served in a specific order, permutations would be used. If the question asks for the total number of ways the customers can be served without considering the order, combinations would be used.

Similar threads

Combination Question on seating
    • Calculus and Beyond Homework Help
Replies
18
Views
1K
Statistics Permutations and Combinations
    • Calculus and Beyond Homework Help
Replies
8
Views
3K
[Discrete 2] Permutation/Combination Question
    • Calculus and Beyond Homework Help
Replies
2
Views
1K
Permutations of taking 2 letters from (a, a, b, c)
    • Calculus and Beyond Homework Help
Replies
8
Views
1K
Permutations (with repetitions) problem
    • Calculus and Beyond Homework Help
Replies
5
Views
1K
MHB #s of Combinations and Permutations of lines?
    • General Math
Replies
1
Views
718
Number of ways of arranging 7 characters in 7 spaces
    • Precalculus Mathematics Homework Help
Replies
8
Views
418
Intro Statistics combination/probability problems.
    • Calculus and Beyond Homework Help
Replies
3
Views
2K
Combinations/Permutations of Seating at a Circular Table
    • Calculus and Beyond Homework Help
Replies
15
Views
4K
Counting permutations of a string with repeating characters
    • Calculus and Beyond Homework Help
Replies
6
Views
2K

Hot Threads

Recent Insights

Back
Top