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Combination and Its Types

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Questions and Answers

In a combination, what is the key factor that distinguishes it from a permutation?

The order of the elements selected (correct)

Whether the selection is random or not

The number of elements in the set

The size of the sample being selected

Which scenario exemplifies a combination with repetition?

Choosing 3 colors from a set of 7, where each color can only be selected once.

Selecting a team of 5 players from a group of 15, where each player can only be chosen once.

Assigning 2 different tasks to 2 different people among 10 employees.

Picking 4 candies from a box of 10 flavors, where the same flavor can be selected multiple times. (correct)

What does 'n' represent in the notation 'nCr'?

The number of combinations with repetitions.

The number of permutations of the set.

The total number of elements in the set. (correct)

The number of elements being chosen.

In a combination without repetition, what is the fundamental restriction regarding the selection of elements?

The same element cannot be picked more than once. (B) Signup and view all the answers

In the context of forming a committee, which of the following scenarios would be a combination without repetition?

Choosing 2 officers from 10 members of a company, where each officer can only hold a single position. (A) Signup and view all the answers

When can a combination with repetition be used in a real-world scenario?

When selecting ice cream flavors with multiple scoops. (D) Signup and view all the answers

How is the combination with repetition different conceptually from combination without repetition?

In the first you can pick the same element multiple times; in the second, that's not possible. (B) Signup and view all the answers

Study Notes

Combination

Combination is a statistical method for finding ways to choose elements from a dataset.
Unlike permutations, the order of elements in a combination doesn't matter.

Combination with Repetition

Elements can be repeated in a combination with repetition.
Example: Choosing 4 candies from 10 flavors, where the same flavor can be picked multiple times.

Formula for Combination with Repetition

(n + r − 1)! / (r! * (n − 1)!)
- n = total number of elements
- r = number of elements to choose

Combination Without Repetition

Elements cannot be repeated.
Example: Choosing 3 people from a group of 20. A person cannot be chosen more than once.

Formula for Combination Without Repetition

n! / ((n − r)! * r!)
- n = total number of elements
- r = number of elements to choose

Examples

Example 1: Choosing 3 out of 8 flavors of candy (with repetition)
8C3 = 120 combinations
Example 2: Choosing 2 shoes from 4 pairs of shoes (without repetition)
4C2 = 6 combinations
Example 3: Choosing 3 shirts from 7 shirts (without repetition)
7C3 = 35 combinations
Example 4: Choosing 3 balls from a set of 10 numbered balls (without repetition)
10C3 = 120 combinations
Example 5: Choosing 4 pairs of shoes from 5 available colors (with repetition)
5C4 = 70 combinations

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Description

Explore the fascinating concepts of combinations, including both combinations with and without repetition. This quiz covers key formulas, examples, and applications of combinations in statistics. Test your understanding of how to choose elements from a dataset, while learning the critical differences between the two types of combinations.