Let's say i have a hand of cards. The number of cards i have in my hand is x > 3. How many unordered different triples of cards can i form with the cards in my hand? Example: i have the following cards in my hand: A B C D i could form, A B C, A B D, A C D, B C D, 4 different triples can be formed.

JetssheetaDumcb 2022-10-28 Answered
Let's say i have a hand of cards.
The number of cards i have in my hand is x > 3.
How many unordered different triples of cards can i form with the cards in my hand?
Example: i have the following cards in my hand: A B C D i could form
A B C
A B D
A C D
B C D
4 different triples can be formed.
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Answers (2)

Spielgutq1
Answered 2022-10-29 Author has 17 answers
You have 𝑥 possibilities to choose the first card, x 1 for choosing the second one and x 2 for choosing the third one. If you multiply these numbers, you get x ( x 1 ) ( x 2 ). However, as you look for unoredered triples, you have to divide this by the number of all possible ordering of 3 cards, which is 3 ! and you get
x ( x 1 ) ( x 2 ) 6 .
Nothe that this is the same as ( x 3 ) , what is exactly what you would expect.
Did you like this example?
Subscribe for all access
bergvolk0k
Answered 2022-10-30 Author has 4 answers
There is a formula and a name. It's called a combination. You should also check out permutations. The notation is ( n 3 ) , or in this case ( 4 3 ) .
In general, the ( n k ) notation means n ! ( n k ) ! k ! . So ( 4 3 ) = 4 3 ! 1 c ! = 4.
Did you like this example?
Subscribe for all access

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

You might be interested in

asked 2021-09-09
In a fuel economy study, each of 3 race cars is tested using 5 different brands of gasoline at 7 test sites located in different regions of the country. If 2 drivers are used in the study, and test runs are made once under each distinct set of conditions, how many test runs are needed?
asked 2021-09-08

A restaurant offers a $12 dinner special with seven appetizer options, 12 choices for an entree, and 6 choices for a dessert. How many different meals are available when you select an appetizer, an entree,and a dessert?

asked 2022-05-27
Prove that ( 2 n n ) = k = 0 n ( n k ) 2
So far I have tried writing the right hand side in different ways: expressing it in its factorial form and have tried to implement the identity
( n k ) = ( n 1 k 1 ) + ( n 1 k )
but have not gained any new ground. If any one has an algebraic proof, or even a simple combinatorics proof that is intuitive and used with an example that would be preferable.
asked 2020-12-17
9 students are in a math class. How many different ways can you choose 6 people for a group?
asked 2021-05-31
Ten red cards and ten black cards are placed in a bag. You choose one card and then another without replacing the first card. What is the probability that the first card will be red and the second card will be black?
asked 2022-11-25
A three-person committee is needed to study ways of improving public transportation. Ho many committees could be formed from the eight people on the board of supervisors?
asked 2022-06-23
Using generating functions one can see that the n t h Bell number, i.e., the number of all possible partitions of a set of n elements, is equal to E ( X n ) where X is a Poisson random variable with mean 1. Is there a way to explain this connection intuitively?

New questions