How many different dominoes can be formed from the numbers 0 …6 ? (Hint: A domino may have the s

step 1 Okay, this question wants us to find out the number of unique dominoes that are in a set, where

How many different dominoes can be formed from the numbers 0...

How many different dominoes can be formed from the numbers $0 \ldots 6 ?$ (Hint: A domino may have the same number of dots on both halves of it or it may have a different number of dots on each half.)

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Combination with Repetition

This concept refers to counting the number of ways to select items from a set when repetition is allowed and order does not matter. In the domino problem, since the same number can appear on both halves, selecting two numbers where the order of selection is irrelevant models a combination with repetition.

Counting Unordered Pairs

When forming domino pieces, each piece corresponds to an unordered pair of numbers because the order of the numbers does not affect the identity of the domino. This idea involves counting pairs where one considers pairs with identical numbers (doubles) and pairs with distinct numbers as a single unique outcome regardless of the order.

Combinatorial Enumeration

This key concept involves systematically counting the ways to combine items under certain conditions or restrictions. For dominoes numbered from 0 to 6, combinatorial enumeration is used to determine the total number of distinct pieces by carefully accounting for all possible arrangements of numbers, including both repeated and non-repeated number pairs.

Transcript

Please give Ace some feedback