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?

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

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

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

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

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

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

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

Flashcards

Definition of Combination

Method to find ways to pick elements from a data set.

Combination vs Permutation

In combination, order of elements does not matter; in permutation, it does.

Notable Expression for Combination

Combinations are expressed as nCr, where n is total items and r is selected items.

Condition for r in Combination

r cannot be greater than n in combinations, as it leads to an error.

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Combination with Repetition

Elements can be selected more than once; e.g. choosing candy flavors.

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Combination without Repetition

Unique selections where elements cannot be picked again; e.g. forming a committee.

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Example of Combination with Repetition

Choosing 4 candy flavors from 10 options where flavors can repeat.

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Example of Combination without Repetition

Forming a team of 3 from 20 employees with no repeats.

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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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Combination and Repetition PDF

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