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

JetssheetaDumcb

Answered question

2022-10-28

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.

Answer & Explanation

Spielgutq1

Spielgutq1

Beginner2022-10-29Added 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.
bergvolk0k

bergvolk0k

Beginner2022-10-30Added 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.

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